In the Link Page to Group plugin, is there a way to make the linked pages that shows up in the group menu show a static title, even though it directs the user to a different page depending on the group?

I would like to add different pages to the different groups but I would like each group’s menu to say the same thing.

Ex: I have “page 1” that is linked to “group 1” and “page 2” that is linked to “group 2”
instead of the page title on the groups showing up as “page 1” and “page 2” in the respective groups menus, I would like to make the page title to be the same no matter what group directs to what page.

So each group will have different pages linked to them but the menu titles in the group say the same thing.

I hope that makes sense.