When writing a business letter my boss has asked me to use "per" in the closing (see example below), even though he signs his own letters. My understanding is that "per" is used if someone else is signing his letters for him. Is that correct?
per John Smith
Correct. Only the signatory's name should be inserted below the signature, unless the letter is signed by another person on behalf of the originator, the abbreviation "pp" is usually used (short for pro persona).