Hi nabilabolo,
Use TempData to send data to other tab.
Set the TempData value in Controller Action Method to pass.
Refer below sample. In the sample i am sending the new generated ID to Material Tab.
Model
public class ItemModel
{
    public string req_name { get; set; }
    public string badge_num { get; set; }
    public string line { get; set; }
    public DateTime req_date { get; set; }
    public int status { get; set; }
}
Controller
public class HomeController : Controller
{
    // GET: Home
    public ActionResult Index()
    {
        return View(new ItemModel());
    }
    public ActionResult AddPlatform()
    {
        return View();
    }
    [HttpPost]
    public ActionResult AddPlatform(ItemModel Imodel)
    {
        RequesterEntities db = new RequesterEntities();
        TempData["Selected"] = "1";
        try
        {
            string id = db.Requesters.Max(x => x.Requester_id);
            string id2;
            if (id == null)
            {
                id2 = "FY21_001";
            }
            else
            {
                string NewID = id.Split('_')[1];
                id2 = "FY21_" + (int.Parse(NewID) + 1).ToString().PadLeft(3, '0');
            }
            Requester model = new Requester();
            model.Requester_id = id2;
            model.req_name = Imodel.req_name;
            model.badge_num = Imodel.badge_num;
            model.line = Imodel.line;
            model.req_date = DateTime.Now;
            model.status = "new";
            db.Requesters.Add(model);
            db.SaveChanges();
            TempData["NewID"] = id2;
        }
        catch (Exception)
        {
        }
        return RedirectToAction("Index", "Home");
    }
}
View
@model Pass_Value_Next_Tab_Button_Click_MVC.Models.ItemModel
@{
    Layout = null;
}
<!DOCTYPE html>
<html>
<head>
    <meta name="viewport" content="width=device-width" />
    <title>Index</title>
    <link rel="stylesheet" media="screen" href='https://maxcdn.bootstrapcdn.com/bootstrap/4.0.0/css/bootstrap.min.css' />
    <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min.css" />
    <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.5.1/jquery.min.js"></script>
    <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min.js"></script>
    <script type="text/javascript">
        $(function () {
            if ($('#hfSelected').val() != '') {
                $("#tabs").tabs({ active: $('#hfSelected').val() });
            } else {
                $("#tabs").tabs();
            }
            $('#btnSaveMaterial').click(function () {
                $('#hfSelected').val(2);
                $("#tabs").tabs({ active: $('#hfSelected').val() });
            });
        });
    </script>
</head>
<body>
    <input type="hidden" value="@TempData["Selected"]" id="hfSelected" />
    <div id="tabs">
        <ul>
            <li><a href="#tabs-1">Details</a></li>
            <li><a href="#tabs-2">Material</a></li>
            <li><a href="#tabs-3">Summary</a></li>
        </ul>
        <div id="tabs-1">
            @using (Html.BeginForm("AddPlatform", "Home", FormMethod.Post))
            {
                <label for="name" class="mr-sm-2">Name:</label>
                <span>@Html.EditorFor(model => model.req_name, new { htmlAttributes = new { @class = "form-control mr-sm-2", style = "width:800px" } })</span>
                <br />
                <label for="email" class="mr-sm-2">Badge Number:</label>
                <span>@Html.EditorFor(model => model.badge_num, new { htmlAttributes = new { @class = "form-control mr-sm-2", style = "width:800px" } })</span>
                <br />
                <label for="phone" class="mr-sm-2">Line :</label>
                <span>@Html.EditorFor(model => model.line, new { htmlAttributes = new { @class = "form-control mr-sm-2", style = "width:800px" } })</span>
                <br /><br />
                <div align="center">
                    <input id="btnSaveDetails" type="submit" value="Save" class="btn btn-primary" />
                </div>
            }
        </div>
        <div id="tabs-2">
            Content for Tab 2 goes here.<br />
            Lorem ipsum dolor sit amet, consectetuer adipiscing elit,
            sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat.
            <br />
            New inserted ID : @TempData["NewID"]
            <br />
            <input id="btnSaveMaterial" type="submit" value="Save" class="btn btn-primary" />
        </div>
        <div id="tabs-3">
            Content for Tab 3 goes here.<br />
            Lorem ipsum dolor sit amet, consectetuer adipiscing elit,
            sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat.
        </div>
    </div>
</body>
</html>
Screenshot
