Alb is indeed for Albatros. The German serial number system was formalised in 1913, and gives some information on identifying this plane:
Alb - Albatros Werke AG, the manufacturer, founded in 1909. Although you'll sometimes see a plane referred to as "an Albatros(s)" that's rather like saying "a Messerschmitt" or "a Boeing", and doesn't indicate the type (e.g. Richthofen himself speaks of flying "my good Albatros"). During WW1 Albatros manufactured over 10,000 aircraft of various types.
C - Two-seat armed biplane scout. There were many other C planes from various manufacturers, and the pilots themselves often referred to their planes using this letter designation. Richthofen himself talks of flying a "C-type" plane in Russia in 1916, possibly a C.III.
III - the manufacturer type in Roman numerals.
Thus to identify a German WW1 plane, you need all three parts. There were, for instance, other Albatros C planes (I - XV); there were other manufacturers' C.III planes (e.g AEG, Halberstadt), and there are other Albatros III planes (e.g. the famous Albatros D.III, where D indicates single-seat fighter). This plane is, therefore, an Albatros C.III .
2143 - the manufacturer serial number
16 - the year the aircraft was ordered (1916)
The Albatros C.III was one of the most important aircraft of the mid-war, one of the first two-seaters with weapons for both crew members. So popular was it that production was spread between Albatros and seven other manufacturers. The aircraft in your picture was built under license by Bayerische Flugzeugwerke, from a batch of 50 ordered in July 1916 (serials 2124 to 2173).
I would speculate that, because this aircraft has no squadron markings it is either about to leave its factory, or just arrived with its squadron. It is also lacking the observer's machine gun. Certainly it's unusual to see a plane in this state, with such a prominent manufacturer's mark and no other markings. So that would make the most likely date for the photo as mid 1916.
I can't say who is in your picture, but here is the Red Baron in front of the same type of aircraft in 1917 (it's definitely not the aircraft in your picture, however, and nor was he flying it: he was just taking a ferry-flight.)