It is preferred that original players resume and finish, however, with timezones etc etc I understand this is not always possible.
You can complete with a "marker" that has already completed round 1 or with a player that is completing their round for the first time (you would be acting as a "marker" for 16 holes and then become "live" in play at the 17th - where you are set to resume. If you act as a "marker" you are still required to save each and every hole by hole score (for verification) of all players in the group.
Should another disconnection occur you follow the same principles as before, making sure that any part card is uploaded onto the thread BEFORE re-commencing.
Hope that answers your question
Good luck