Thank you for the information. I assume you are asking if this might be a scam. I can tell you without reservation, that it is. There is no such thing as a "leave bonus" in the Navy, or any other U.S. military service. They are asking you for money, they are just doing it in a very creative way.
Also, there is never a requirement that anyone write a letter to the Command to ask for leave for the servicemember. In fact, the Command would ignore such a letter, as it is the servicemember and the Command that make that decision. The only exception is in cases of humanitarian leave when someone in the immediate family has died or is gravely ill. In that case, the Red Cross sends a message.
These cyber criminals are very good at what they do and have taken on the identity, in most cases, of a real soldier, sailor, Marine or airman. They steal their pictures and background information from social media and make up what they don't know about the servicemember.
This is a classic scam and you can read more about these types of scams and how to report them by going to: http://www.cid.army
Just to make sure that you understand, that if you send these people money, you will never see them or your money again.
Please let me know if you need any clarification.