One way to draft the letter would be to point out the incredible opportunity that staying for another week in Oman would give to your son.
I'm assuming that your son speaks English, and that many of the people he would encounter in Oman do not. If this is true then speaking with those around him would help him hone his English-speaking and writing skills. Also, by staying the additional time in Oman he would have more experiences to write about in his classes when assignments are given by his teachers.
Also, most students lack any realistic awareness of countries that they don't have contact with. By staying in Oman he would continue to expand his awareness of the country he is living in by being able to compare it with what he has experience in Oman. In short, he could easily become an unofficial but believable ambassador while he is a student, and potentially a life-long representative, for both countries.
