Addon "button group" Joomla does not work correctly through Wrapper

Using Addon "button group" I created an internal menu for the landing, but when I embed it through Wrapper into another site, the menu buttons on it do not move to a position, they do not react at all to pressing.

They only work if you check the box "open in a new tab"

For the internal menu, in the link field I insert the section ID with the hashtag. For example #projects . And this works for a smooth transition to the desired section on the landing page, but if you embed this landing page in another site, it no longer works.

Can you please tell me how to make this work? Maybe you need to specify the link to the section in some other way so that it works when embedding this page through Wrapper ?