Inverse of "Add Friends to Activity": Allow users to *request* to re-post an activity that they completed with a friend. This would be for occasions when a user forgets to record their activity, but a friend did. User would go to a friend's activity and click a new button: "Request to Join Activity"
EXAMPLE: I'm often doing a group run where I don't bring my GPS watch. However, my friends who did record usually forget to add me via "Add Friends to Activity" when they post to Strava. If I could "re-post" or "join the activity" that a friend had posted, they would get a notification to add me and I would get more accurate records of these activities.
NOTES: Not all stats would be transferred from your friend's activity to the one posted on your page... I imagine only the map, duration/pace, splits would. Performance on a segment wouldn't transfer, and personal stats like heartbeat, etc. wouldn't transfer. The friend could also choose to reject the request (e.g., maybe you didn't actually run the whole activity at the same pace as your friend).