Since it isn't explained in the episode, I think we can extrapolate from the space bees' and wasps' real-life equivalents - there are species of wasps that prey on bees, called beewolves.
We're shown the remains of the previous Planet Express crew still in the hive, so obviously their bodies weren't completely consumed but presumably as the bodies rotted the chips came loose. They could then have adhered themselves to a bee given all the space honey around.
That bee, when leaving the hive to collect space pollen, was attacked and consumed by the space wasp, including the chips that were attached to it. When the space wasp is killed, the chips were found in its stomach and sent to the Professor labelled as such.
As for the chips being sent to the Professor, there isn't much information on what is contained in career chips. We can assume employer isn't part of it, as we see Fry having his inserted as "delivery boy" even prior to Fry obtaining a job. If we suppose that the implantees' names are part of the information, it becomes fairly simple - a bit of research on names can yield their employer, and from that point it is merely a delivery issue.
If that assumption is not made as to the contents of the chips, the most likely explanation is that whoever "obtained" the space wasp's stomach contents was aware of the Planet Express ship entering the hive and reasonably assumed that the chips belonged to them. That could have been someone in the locality of the hive at the time or someone the Professor hired to recover the chips.
Either way this is all supposition as I do not believe a canon answer has been provided.