March 2021 update : I still have not had any luck locating any software for this.
This device differs to the Amstrad CPC Multiface for example as it does not have its software stored in a ROM chip. From a photo of the PCB, apart from the logic ICs, the only other IC is a HM6264LP-15 SRAM IC. This SRAM chip is a 64 K ( 8-kword X 8-bit ) IC.
Unfortunately, the Action Replay did not come with any software. I have checked several sites online and I am unable to locate a disk or tape image of the software. The only download that I can find is a copy of the PCB in Eagle format by Jose Leandro.
If you have a copy of the software, I would really appreciate it if you could send a copy to me. You can contact me via the social media links to the right of this page.
There is more information and photos about the Action Replay on this CPCWiki page : Action Replay AMX