It wouldn't be a matter of Bush the first doing it because it was "difficult" to appoint his own man. Bush senior was a very courteous individual, and he was, unfortunately, too moderate. That is why I wondered if the ambassador was appointed late in the year (the only date given was the year) , he went ahead and consulted with the next admin. He did it on other things as there was a normal and well planned transition when he handed over the reigns to the next administration. The transition process does begin - or should- before a president leaves office.
But as someone discovered just before your post, the Ambassador was appointed in May of 92, not late in the year, so no, I now doubt it was a matter of courtesy since this would be well before the election and it wouldn't make sense. Looks more like he's just a career State Dept. employee (been in there since 76) who was just moved on up to an ambassador's position. I don't think Bush Sr. was the type to clean house as the Clintons did with state's attorneys and the travel office. If someone was due an advancement they probably got it.