Populate Field Group With Fields From Another Field Group
No, there's nothing built into Craft that lets you do this. 

Please note though, that you can reuse fields across sections in Craft. Field groups is just an organizational layer on top of fields to make it easier to add a group of fields to a section, and to be able to find fields more easily. It doesn't give any additional meaning to the fields. So you can't have a field with the same handle in different field groups, and it doesn't make sense to duplicate a field that's actually used across sections.

If you need to duplicate fields (because they're actually suppose to be different fields), I highly recommend the Field Manager plugin by Verbb (Craft 2 and Craft 3 versions available) which makes it super easy do to this, and in general provides a much better interface to manage fields.