Did I rewrite this sentence correctly?

[Vkhu]

I was told to rewrite the sentence using the word passed

They didn't reply to my letter for two months
->Two months passed by before they replied to my letter

Did I got it right? It was taken from the book Use of English by Mark Harrison but my key page got ripped out. Some one check it for me.

[Dozy]

This is OK (except for the missing full stop at the end of the sentence).

It would also be OK without "by".