Just in case someone else runs across this question:
1) You could ask them to send the sharing link from you specifically, instead of sharing a general link.
2) You can export your GEDCOM file and reimport it as a new family. One of the steps in that process is to say which family member is the founder. Note that pictures are not exported. Of course, this would be a new family tree, and would not be updated when the original is updated.