Dear XXX,
How are you? It has been a long time seen we last had contact.
I am very busy with my studies recently. I have been putting in a lot of effort in learning English. My vocabulary has improved a great deal. However, I think that my grammar still has much room for improvement, so I would like you to help me buy English grammar books. Please find some that are suitable for my standard. Thank you so much!
Also, please come and visit anytime when you are free! Just give me a call.
Yours sincerely,
XXX