During his two-year prison stint

[Bassim]

I am wondering if my sentences are grammatically correct.

During his two-year prison stint, Michael wrote his wife every week. She read and reread the letters countless times and kept them like treasure.

 

[emsr2d2]

In BrE, it would have to be "Michael wrote to his wife every week". In AmE, your version is OK, as far as I know.
I'm not keen on "kept them like treasure". I'd probably use "treasured them".