добавляю тестовые скрипты на всякий случай

app/Http/Controllers/TestFormController.php

@@ -0,0 +1,25 @@
+<?php
+
+namespace App\Http\Controllers;
+
+use App\Models\TestFormModel;
+use Illuminate\Http\Request;
+
+class TestFormController extends Controller
+{
+    public function getForm()
+    {
+        return view('test_form');
+    }
+
+    public function setForm(Request $rqst)
+    {
+        $testTable = new TestFormModel;
+        $testTable->first_name = $rqst->first_name;
+        $testTable->last_name = $rqst->last_name;
+        $testTable->department_name = $rqst->department_name;
+        $testTable->save();
+
+        return redirect('/test_table');
+    }
+}