Implant #12 too close to tooth#13?

Based on the X-ray I would advise removing the supra erupted middle tooth which has about 50% bone around it. It can be used to protect the implant while it is osteointegrating. The placement is not the issue, it is the prosthetic plan. You can let the patient know that #13 is the problem not the implant and future extraction will be necessary negotiate a price on the bridge since trying to place a crown here will be difficult and you'll be removing 13 in the future and then another implant will be needed. The patient will be happy about the savings. No harm in the surgery just difficult sales job, patient's don't dictate the treatment. Be very careful since you are playing catch up here, bottom line this is a non restorable tooth regardless of the implant placement. Learn from this since it is the patient's desires that put you in a corner now and removal of 13 would have been better at implant placement this there is some risk in removal next to an integrating / integrated implant. You worked very hard in this difficult but well placed implant but that middle tooth will be a problem in the future trust me. Good Luck.

If you do not extract tooth #13, the periodontal disease on this tooth will compromise the periodontal status of the implants, especially the distal one. Extraction is strongly indicated and then a 3 unit fixed bridge.

First of all, it is very difficult to accurately tell distance between implant and tooth from a periapical radiograph. It is dependant on the angulation you take it at. CRS, I do not quite understand why there would be a prosthetic issue? Implant is very well angulated down long axis of a future implant crown and I do not see an issue with restoring this implant (may have to thin down the impression coping a little narrower, but doable).