Is it grammatically correct to say - here is a copy of the email between Sally and me?

No, that's not grammatically correct. The correct way to say it is:

Here is a copy of the email between Sally and me**.

Here's why:

* "Between" is a preposition, and prepositions are followed by objects.

* "Me" is the object form of the pronoun "I".

* "I" is the subject form of the pronoun.

So, the sentence should read "between Sally and me" because "me" is the object of the preposition "between".