Since the pharmacist already declined your Facebook request, I really would not ask him out either in person or via letter. He is there to do a job, and by rejecting the fb request he has already let you know he is not interested in a more personal relationship. If he rejected the fb request, saw the message on messenger and then gets asked out, he might decide that constitutes harassment and you may be asked not to come back to the pharmacy. Is it really worth risking being banned from the pharmacy just to give him a letter, knowing he's going to say no anyway? Even more so, if you really care about this guy, why put him in the position of making him feel uncomfortable and having to turn you down? It has nothing to do with you not being pretty (I'm sure you are) or not being a great person (I'm sure you are). He seems to simply not be interested. For all we know he may already be in a relationship, or just not be interested in anyone who has ever been a client, even if they're not a client anymore. Why not put your energy into more positive, self-enhancing activities? Maybe try studying the material in order to take the test again, or get more involved in hobbies, or spend time with other people whose company you enjoy?