Hello,
You can't create a single Home Page Action for this purpose, but you can workaround with the help of two Custom Commands. One of the Custom Commands will copy the group memberships from a user to a virtual attribute of the user who launches the Custom Command, and another one that will 'paste' the group memberships stored in the virtual property to the user, on which the Command is executed. In other words, the first Custom Command needs to be executed on the user whose memberships are copied, and the other one must be executed on the user(s) to whom the group memberships will be copied. For details on how to create such Custom Commands, take a look at Copy of groups membership from one user to another.
If necessary, you can make the Custom Commands available on the home page as Home Page Actions. For details, see section Custom Command in the following tutorial: http://www.adaxes.com/tutorials_WebInte ... #executecc.