The Z230 SFF workstation has a serial port on the backplane and a special serial port header on the motherboard, but the tower version seems to only have a single special serial port header on the motherboard..... I bet you have the tower version.
HP has some complex part numbering systems, Spares P/N, Assembly P/N, Options P/N, so you may need to search under any of those three, and the same part can be given a different set of numbers as it is used in a later workstation. That is the case for you..... but the Options P/N stayed the same.
Many of the HP workstations have had a single external serial port adapter on the backplane, and a proprietary header on the motherboard so the owner can add a second serial port. If no serial port was on the backplane the adapter still has kept its same name of "HP 2nd Serial Port adapter".
You want both the adapter and the cable. You can't just hook up a "pass-through" adapter. There is an actual circuit board attached to the adapter bracket that HP designed, and a special ribbon cable to go from that to the motherboard header. In some of the HP documents they actually have the wrong picture of the adapter (those documents show incorrectly a pass-through ribbon cable). I'll add the correct picture below.
Here are some numbers for the device I have been using with my xw workstation and Z620 work:
PA716A (Options P/N) ...this is listed in the Z630 QuickSpecs document as the one you need.
283984-001 (Spares P/N)
264534-001 (Assembly P/N)
You'll find the most on eBay under that Options P/N of PA716A. Never buy one without the ribbon cable..... you will not find those available by themselves. If you search under then part number you provided you'll likely get sticker shock, but off eBay the PA716A is going for about $15.00 USD. My guess is that you don't need the SFF backplane bracket included in some of the kits shown there.
For me this adapter is plug and play..... the OS drivers built in just work.
Keep us posted on this.... there still is a need for serial ports for some of us, and the right price counts. Here's that correct picture of what you need:
