If the cable your fixing is prebuilt, my guess is that it won't be wired A or B. Purchased cables usually just match the colors. Just make note of what order is there and match it on the other end like belvdr said. If you can't tell, cut the end off and replace both ends.
P.S. It doesn't really matter if you use A or B (or any other order for that matter) when wiring a new cable, just use the same order for both sides. If you need a crossover cable, use A on on end and B on the other.
You should use solid for a punchdown. Stranded might work, but it won't be a good connection.