Responding to your question I've made some changes to your code, basically it would look like this:
First let's change the way you are thinking about your code, instead of removing the row of the Here button, let's just hide it. that is, we comment the line; $(this).parent().parent().remove(); and add var tr = $(this).closest("tr"); . In the end you should have something like this:
// $(this).parent().parent().remove();
var tr = $(this).closest("tr");
and then we add the code that I leave below in the button with the class; .btneli
$('tr .btneli').one('click',function(){
$('.btneli').parent().remove();
var tr = $(this).closest("tr"); //con la función closest llegamos hasta el tr
var td = $(tr[0]).children(0); //Solicitamos el primer TR y obtenemos su primer hijo TD
var texto = $(td[0]).text(); //Extramos el texto del TD
$(".table tr td:contains("+texto+")").closest("tr").show(); //Buscamos el TD que contenga el texto, subimos hasta el TR y mostramos toda la fila.
});
Likewise I leave you the Snippet.
$('.a').one('click',function(){
$(".othertable").append("<tr><td>"+
$(this).closest('tr').children()[0].textContent+"</td><td><input type='text' placeholder='Ingresar cantidad'/></td><td>"+
$(this).closest('tr').children()[1].textContent+"</td><td><input type='button' class='btneli' value='Eliminar'></td></tr>");
// $(this).parent().parent().remove();
var tr = $(this).closest("tr");
$(tr[0]).hide();
$('tr .btneli').one('click',function(){
$('.btneli').parent().remove();
var tr = $(this).closest("tr");
var td = $(tr[0]).children(0);
var texto = $(td[0]).text();
$(".table tr td:contains("+texto+")").closest("tr").show();
});
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<!-- Latest compiled and minified CSS -->
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/css/bootstrap.min.css" integrity="sha384-1q8mTJOASx8j1Au+a5WDVnPi2lkFfwwEAa8hDDdjZlpLegxhjVME1fgjWPGmkzs7" crossorigin="anonymous">
<!-- Optional theme -->
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/css/bootstrap-theme.min.css" integrity="sha384-fLW2N01lMqjakBkx3l/M9EahuwpSfeNvV63J5ezn3uZzapT0u7EYsXMjQV+0En5r" crossorigin="anonymous">
<!-- Latest compiled and minified JavaScript -->
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/js/bootstrap.min.js" integrity="sha384-0mSbJDEHialfmuBBQP6A4Qrprq5OVfW37PRR3j5ELqxss1yVqOtnepnHVP9aJ7xS" crossorigin="anonymous"></script>
<div class="row">
<div class="col-xs-12 col-md-12">
<table class="table table-condensed table-hover table-bordered">
<thead>
<tr>
<th>Firstname</th>
<th>Lastname</th>
<th>Accion</th>
</tr>
</thead>
<tbody>
<tr>
<td>John</td>
<td>Doe</td>
<td><button class="a">Aqui</button></td>
</tr>
<tr>
<td>Sam</td>
<td>Smith</td>
<td><button class="a">Aqui</button></td>
</tr>
</tbody>
</table>
</div>
</div>
<table class="othertable table-condensed table-hover table-bordered">
<thead>
<tr>
<th>Firstname</th>
<th>Precio</th>
<th>Lastname</th>
<th>Accion</th>
</tr>
</thead>
<tbody>
</tbody>
</table>
<div class="modal fade" id="myModal">
<div class="modal-dialog">
<div class="modal-content">
<div class="modal-header">
<button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button>
<h4 class="modal-title">EDIT</h4>
</div>
<div class="modal-body">
<p><input type="text" class="input-sm" id="txtfname"/></p>
<p><input type="text" class="input-sm" id="txtlname"/></p>
</div>
<div class="modal-footer">
<button type="button" class="btn btn-default" data-dismiss="modal">Close</button>
<button type="button" class="btn btn-primary">Save changes</button>
</div>
</div><!-- /.modal-content -->
</div><!-- /.modal-dialog -->
</div><!-- /.modal -->
Update by comment tracking.
Well, I'm going to leave you a code that I made based on the particular need.
It should be noted that there were many things that I did not work with Jquery, I did in JS Nativo, this because of the ease of the native JS.
$('.a').on('click',function(){
var trPrincipal = this.offsetParent.parentElement; //Buscamos el TR principal
var firstName = trPrincipal.children[0].outerText; //Capturamos el FirstName
var lastName = trPrincipal.children[1].outerText; //Capturamos el LastName
$(".othertable").append("<tr><td>"+
firstName+"</td><td><input type='text' placeholder='Ingresar cantidad'/></td><td>"+
lastName+"</td><td><input type='button' class='btneli' value='Eliminar'></td></tr>");
trPrincipal.style.display = "none"; //Ocultamos el TR de la Primer Tabla
var btn_ = document.querySelectorAll(".btneli"); // Buscamos todos los elementos que tengan la clase .btneli
for(var a in btn_){ //Iteramos la variable btn_
var b = btn_[a];
if(typeof b == "object"){ //Solo necesitamos los objetos
b.onclick = function (){ //Asignamos evento click
var trBtn = this.offsetParent.parentElement; // buscamos el tr principal de la segunda tabla
var firstNameBtn = trBtn.children[0].outerText; //Capturamos el FirstName de la segunda tabla
trBtn.remove(); // eliminamos toda la fila de la segunda tabla
var tbl = document.querySelectorAll(".table td:first-child"); //Obtenemos todos los primeros elementos td de la primera tabla
for(var x in tbl){ //Iteramos los elementos obtenidos
var y = tbl[x];
if(typeof y == "object"){ //solo nos interesan los object
if (y.outerText == firstNameBtn){ //comparamos el texto de la variable y vs el firstNameBtn
var t = y.parentElement; //capturamos el elemento de la coincidencia
t.style.display = ""; //actualizamos el estilo display dejándolo en vacío y esto mostrará nuevamente la fila tr de la primera tabla
}
}
}
}
}
}
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<!-- Latest compiled and minified CSS -->
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/css/bootstrap.min.css" integrity="sha384-1q8mTJOASx8j1Au+a5WDVnPi2lkFfwwEAa8hDDdjZlpLegxhjVME1fgjWPGmkzs7" crossorigin="anonymous">
<!-- Optional theme -->
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/css/bootstrap-theme.min.css" integrity="sha384-fLW2N01lMqjakBkx3l/M9EahuwpSfeNvV63J5ezn3uZzapT0u7EYsXMjQV+0En5r" crossorigin="anonymous">
<!-- Latest compiled and minified JavaScript -->
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/js/bootstrap.min.js" integrity="sha384-0mSbJDEHialfmuBBQP6A4Qrprq5OVfW37PRR3j5ELqxss1yVqOtnepnHVP9aJ7xS" crossorigin="anonymous"></script>
<div class="row">
<div class="col-xs-12 col-md-12">
<table class="table table-condensed table-hover table-bordered">
<thead>
<tr>
<th>Firstname</th>
<th>Lastname</th>
<th>Accion</th>
</tr>
</thead>
<tbody>
<tr>
<td>John</td>
<td>Doe</td>
<td><button class="a">Aqui</button></td>
</tr>
<tr>
<td>Sam</td>
<td>Smith</td>
<td><button class="a">Aqui</button></td>
</tr>
</tbody>
</table>
</div>
</div>
<table class="othertable table-condensed table-hover table-bordered">
<thead>
<tr>
<th>Firstname</th>
<th>Precio</th>
<th>Lastname</th>
<th>Accion</th>
</tr>
</thead>
<tbody>
</tbody>
</table>
<div class="modal fade" id="myModal">
<div class="modal-dialog">
<div class="modal-content">
<div class="modal-header">
<button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button>
<h4 class="modal-title">EDIT</h4>
</div>
<div class="modal-body">
<p><input type="text" class="input-sm" id="txtfname"/></p>
<p><input type="text" class="input-sm" id="txtlname"/></p>
</div>
<div class="modal-footer">
<button type="button" class="btn btn-default" data-dismiss="modal">Close</button>
<button type="button" class="btn btn-primary">Save changes</button>
</div>
</div><!-- /.modal-content -->
</div><!-- /.modal-dialog -->
</div><!-- /.modal -->