PTSD can take so many different shapes and forms and it does effect everyone differently. The way that traumatic events mess with our brains can impact the brains ability to form new memories. Thankfully though, there is more and more research out there that shows that the brain can change and with help he may be able to restore the ability to form new memories and work with them in the short term. Memory is a very complex thing and figuring out the cause for the difficulties with short term memory problems would be beneficial. This can be done through MRI and FMRI imaging. It sound like he also has several other problems that may be more problematic for your relationship in the long term. It may be beneficial for you guys to seek counseling together. It may help him warm up to the idea of therapy if he knows that you will be there with him. I hope this information helps.
-Apathetic Superhero