The school cannot diagnose your child. They can try to address the issue with extra help, etc, but my recommendation is that you talk to your pediatrician about the problems he seems to be having with memory. I believe your pediatrician will recommend that you obtain an outside evaluation for your son to hopefully determine exactly what is going on. A lot of children receive extra help in certain areas. They may pull him out of the classroom for extra help if they need to, but he won't be the only one. Some children even receive the help of an aide in the classroom to ensure the child's success.
His memory issues have to be significant enough for them to just agree to an IEP and services. Never assume that they will give him EVERYTHING that he needs. Budgets are very tight right now, and we no longer have "maximum feasible benefit." By having an outside evaluation done, you can determine exactly what he needs. You can then call a team meeting with school personnel (always put it in writing, have it date stamped and save a copy as they must respond to you within a certain period of time) to discuss the findings and recommendations that you have received from an outside evaluation. An outside evaluation takes some time, so I would recommend that you review and sign your IEP so that he will receive services ASAP. The most important thing is that he receive the assistance required to be successful. Children that are very bright but are having difficulties sometimes become extremely frustrated.
As far as a school that deals with memory issues, I'm not aware of any, but you would also be taking your child out of his neighborhood school where all his friends go and putting him in a school somewhere else. Plus, you do not really have a true diagnosis. No school district will just automatically agree to outplacement as it is extremely expensive.
I am not sure where you live, but I do know that towns are supposed to have PACs. I am from Peabody, and we have the Peabody Parents of Children with Special Needs. They have monthly meetings with very informative speakers on a variety of topics. At those meetings, you meet many, many parents, some of whom may have gone through exactly what you're going through. There is a wealth of information to be gained by networking with other people. By the way, anyone can attend our meetings (i.e., you don't have to be from Peabody).