In Core Share, currently, Android application has no option to share a file or folder via its own menu.
An Enhancement Request has been submitted to Product Management for review of this request.
Not sure if I am understanding the use case, but you can indeed share/collaborate via the "more menu" (looks like three dots "ooo") next to the file. Tapping "Collaborate" will bring up either a) a list of collaborators or b) an option to invite collaborators -- this depends on the permissions granted to the user.
Via this method, I can invite additional collaborators/share the folder or file so long as I have sufficient permissions granted.
Please make sure that you are running the latest available version of the app for Android by visiting the Google Play store and searching "OpenText Core"
Sr. Communications Specialist