It works, thank you. What I have done: (1) Add "REGISTER_APP_GROUPS" to the main app and widget targets (2) Remove "App Groups" capabilities from the two targets (3) Add "App Groups" capability to the two targets and add a NEW group name (4) Close XCode (5) Delete all files from ~/Library/Developer/Xcode/UserData/Provisioning Profiles (6) Open Xcode -> Clean -> Archive -> Upload

They are different questions, and as in Feedback FB18792279 "Apple" said "It is recommended you submit a separate post for each question unless your inquiries are closely related."