I haven't heard of an FAA legal opinion on this, so I'm just guessing here...

I don't think there is a legal requirement for an instructor to personally make a pen-and-ink endorsement in your logbook. Since "logbook" is not legally defined in the FAR's, your logbook could be anything you want it to be...a collection of loose papers, a three-ring binder, a paper towel, whatever. A fax endorsement SHOULD work fine, but I would probably replace it with the signed original asap...future employers tend to prefer unambigious records.

However...I would think that a required endorsement on a student pilot certificate might be a different story. The student certificate IS clearly defined in the FAR's, and if the FAR's say you need to endorse it, a fax might not be sufficient in the eyes of some Feds. Or if you do the fax, follow up with a pen-and-ink immediately upon returning.