That is not always the case, the voltage stored in the EPROM could be the same and it will work just fine, some miners like the S9k had the type ID printed on the hash board itself, some of the S17 series have the type id in the kernel log, so the seller can pre-program the dashboard before shipping it.
OP, the most component of the miner that fails is the hash board, it's very hard to find hash boards of very old miners like the S9s, it will be extremely difficult to find any for S19 pros, even if you do, the price will likely be way too high, not telling you to dismiss the idea, but keep your expectations as low as you can afford.
Keep in mind that these hash boards are sensitive, it will be very hard to ship them securely, it's always best to buy a hole miner and use its component as spare parts, but this of course only makes sense if you have a few miners and not just one.
Plan B would be to send them for repair, which will most certainly be a lot cheaper than obtaining a replacement hashboard.