I am at a loss as to how to begin to start this post. I can not begin to express to you my sincere condolences for your loss. Having lost my sister I DO know what you are going through. We kept her phone active with it's outgoing ("This is Donna I'm not available right now, please leave me a message") for several years after her death for JUST that reason. We listened to that so often.
Unfortunately there is no way that I know of to retrieve that facetime call. They are not saved locally or on any servers that I am aware of. Cherish the memories you have of him. Recall the times shared, and the memories good and bad, and never forget. Know that while it NEVER goes away, it does get easier with time! (You have me crying and thinking about my sister as I type this)