TL-SM321B and TL-SM321A are necessary because two different wavelengths are used for RX and TX and this on the same fibre ! I was able to simply switch TL-SM321B to a MICROTIK router (INIT7 - FIBER7 provider).
No, I don't think this module works with the HP 1820-24G. I also fell on my face. It was not recognised by my HP 2530-8G-PoE+.
I finally ordered the SFP module from Fiber7, their response was:
"We can supply optics + patch cable for CHF 77.00 and program the optics from Flexoptix to HP. Please note this accordingly on the order form."