HP firmware in the SFP module, so it could not be changed to Cisco or other compatible??

[thankfly]

A module wants to compatibal with HP, you need to write a special firmware into MCU.

So why it works fine when you read an original HP SFP and then write this it's code into 3rd party, but does not work when you write it to exactly the same hardware?
By the way I do a lot of SFPs for Extreme Networks 10G on Finisar FTLX8571BCL (I found Extreme Networks uses FTLX8571BCL), I also did a few succesful writes on HP 40G QSFPs on Finisar FTL410QE4C. And these all works fine clonned that way.

There is no sense to copy an eerpom from orginal module to a 3rd-pary module, even this module is the same brand.

I don't understand your point - all the 3rd party's SFPs has the eeprom content from original HP. And that works, right?
Do you mean some different MCU code (not generic, but HP specific) + HP eeprom code?

HP SFP(Speed under 10G) use HPidV1, and only check SFP eeprom.
HP SFP+(Speed above 10G) use HPidV2, it not only check SFP+ eeprom, but also MCUs.
It is totaly different.
Hope helpful.