Not quite USB to PS/2 but pretty close, although I don't know much about AMX mice.
https://www.waitingforfriday.com/?p=827
SmallyMouse2 is a universal USB to quadrature mouse adapter for many 8-bit and 16-bit retro computers and allows the use of modern USB mice on machines such as the Acorn BBC Micro, Acorn Master, Acorn Archimedes, Commodore Amiga, Atari ST and many more. Unlike most existing mouse adapters, SmallyMouse2 implements a fully USB compatible interface (most current adaptors are PS/2 based) this allows the use of any modern mouse including those that use wireless communications.
https://hackaday.com/2017/06/12/a-universal-u … rature-encoder/
The design of the SmallyMouse2 uses an AT90USB microcontroller that supports USB device and host mode, and allows for a few GPIOs. This microcontroller effectively converts a USB mouse into a BBC Micro user port AMX mouse, generic quadrature mouse, and a 10-pin expansion header. The firmware uses the LUFA USB stack, a common choice for these weird USB to retrocomputer projects.