I was in this same situation (without the cheating history) a few years ago, when I was still dating DH. I got a small, extremely pretty arrangement of roses on my birthday. The card said, "From someone who loves you."
I immediately called DH, then-BF, and thanked him profusely for being so thoughtful. He was confused, as he did not send me any flowers. He said, "Who else would send you flowers?!" I said, "Hmm, it was probably my mom or grandma or something. I'll call around and ask."
It turned out to be a male friend from college who had already professed his love for me and wanted me to leave BF (to whom I was engaged) and "paint the world with all the colors of my soul." And of course, he wanted to be the one handed me the paints, even when I told him I wasn't interested. Part of me still wonders if he sent the flowers anonymously, just to start trouble. Either way, I broke off the friendship and I was honest with BF about what happened. It wasn't easy, BF did not like this friend, and got upset when he heard what happened. But, if I'd been dishonest, it would have made BF suspicious and caused more trouble than a bunch of silly flowers was worth.
Bill needs to thank Jill, just in case, and if she didn't send the flowers, just shrug and say, "Huh, maybe the florist made a mistake." He should not make more of an ordeal of this than it's worth.