Apple - Any way to move contacts between groups on iPhone?
Go to "groups" in "Contacts" and uncheck all the groups except the one the contact you want to move is in.
Search for the contact you want to move and "Share" the contact to your own email address or phone # via text.
Click "edit" on the contact you just sent and delete it.
Go back to Groups and uncheck the group the contact was sent from.
Leave only the Group you want the contact in checked.
Go to your email/text and import the new contact. It will automatically be added to the only active group which you selected.
Go back to Contact Groups and select all the groups you want showing on your phone.
Voila!
This cannot be done on the phone. You can sync your contacts to a Mac and do the changes from Address Book on the Mac.
You can also do this via iCloud.com.
Use Orbi Tools. Can be downloaded from App Store.