I have a login menu with some menu items that are only visible after you have logged on with the user name and password.
This works on the PC, so that the login menu only shows after the users have logged in.

I have added a login menu to the template, but when I log in I don't see the Login menu on the template.
The template only show the basic menu.

Is there some way to change or increase the menu shown after the users have logged on?

By default, the Mobile Joomla system only creates a mobile copy of the Main Menu. Have you created an additional Menu Module for the logged in menu for mobile? If you look at your modules, you will see your main menu located in whatever position you chose (1,7, etc...) and a mobile menu located at mj_all_header. If you open the properties for the mobile menu you should see it assigned to the Main Menu via the dropdown box for Menu Name.

Create a New Module, select Mobile Menu from the module type, assign it to mj_all_header, set the proper access level, and then in the Menu Name list on the right, select the menu name for your logged in menu you want to display.

Hope this helps you.

Thanks!
it works now, so I can continue to fine-tune the mobile version of the website!

Glad I could help.