In the sentences
A copy of your documents has been emailed to firstname.lastname@example.org.
A copy of your documents have been emailed to email@example.com.
I believe the subject is "copy", and since "has" refers to the third person singular ("it" being "copy") I believe the first sentence to be correct. Does the preposition change the focus of the subject to "documents" or does it remain singular ("copy")? I don't think the subject has become "documents" at any point in the sentence.
Even if there were multiple items after the "of", such as
A copy of your documents and files (has/have) been emailed to firstname.lastname@example.org.
would the subject still be "copy" or is it now the items?