Implant to fill the hole of a broken molar OR bracing the molar behind forward to cover the hole? (photo)

regardsI recommend placing an implant, bringing a molar to the position you need takes a long time and a lot of work, placing an implant is simpler and less traumatic, the upper molar as only 2mm down with a simple adjustment is enough.I wish you the best

The distance to move the second molar into the first molar position is too far.  Your best option is implant the first molar and possibly shave the opposing tooth in order to make room for the crown space.  

You can get an implant in that area after 4 or 5 months the crown… in case you want the other option is good too just is going to be a treatment longer. 

This is a very interesting question. If enough bone is available to move the tooth forward, then that would be a nice option. It could be a difficult movement; so make sure the dentist has plenty of experience. The natural tooth would be better than an implant in the long term though an implant is a pretty nice alternative for a natural tooth. Either way you need to evaluate the bone using a CBCT type of catscan x-ray before you do anything.