With a future update, it will be easier to accomplish this task. But in the meantime, please follow these steps:
- Go to Contacts Sync > Contacts > Groups, and select the destination group
- Press "+", and select "Add Existing Contacts". You should now be on the "Add Contacts" screen.
- Next, you can optionally remove all existing group members by pressing the "None" button at the the bottom. Then press "Save"
- Next, press the group filter button at the bottom (the button that looks like a group of people). Then select the source group. Then press "Save"
- Press "All" to add all of the contacts in the source group to the destination group. Then press "Save"