Sub Авторизация()
 Dim IE As Object
 Set IE = CreateObject("InternetExplorer.Application")
    IE.Navigate "тут сайт"
    IE.Visible = False
    IE.Navigate ("и тут сайт")
    
    Do Until IE.ReadyState = 4 'For STATE as COMPLETE
        DoEvents
    Loop
    Dim a As String
    Dim b As String
    a = Sheets("Лист1").Range("A1")
    b = Sheets("Лист1").Range("B1")
    
    IE.Document.getElementByID("username").Value = a
    IE.Document.getElementByID("password").Value = b
    IE.Document.getElementByID("rememberMe").Click

<form name="f" action="j_spring_security_check" method="POST">
    <table>
        <tr>
            <td><label for="username">Логин</label></td>
            <td><input type="text" name="j_username" id="username"
                       value=""/>
            </td>
        </tr>
        <tr>
            <td><label for="password"> Пароль</label></td>
            <td><input type="password" name="j_password" id="password"></td>
        </tr>
        <tr>
            <td>
                <input type="checkbox" name="_spring_security_remember_me" id="rememberMe">
            </td>
            <td title="Не спрашивать пароль две недели">
                <label for="rememberMe">Запомнить</label>
            </td>
        </tr>

        <tr>
            <td colspan='2'><input name="submit" type="submit" value="Вход"></td>
        </tr>
    </table>
</form>