While it is not possible to select individual - existing - photos from your Aura app's 'Photos' section to transfer them to another frame, you can transfer entire photo updates from your 'Activity' section as long as you (not a contributor) had uploaded those photos in the first place. This means that any update in the activity feed - and the linked photos - will be transferred to a different frame:

• Go to the selected frame's ACTIVITY screen (1)
  
  
• Scroll down and select an activity update that you would like to transfer to a different frame that you are invited to. 
  
  
• Click on the ". . ." button next to the photos (2) 
  
  
• You can now copy all photos that had been part of this 'activity update' and send them to another frame: