Users rarely need firmware; they need CPS. The most common version for the GP340 is Motorola Professional Radio CPS R06.12.05 or later (often referred to as "Commercial Series CPS").
The software required to program the Motorola GP340 is part of the Professional Radio CPS (Customer Programming Software) series. It is often referred to simply as "GP300/GM300 software" or "Professional Radio CPS R05.xx." motorola gp340 software
Unlike modern radio software which is often cloud-based or driver-heavy, the GP340 software is a lightweight, offline application. Its primary function is to act as the interface between a computer and the radio’s internal logic board, allowing the user to define how the radio operates. Users rarely need firmware; they need CPS
If you buy a USB programming cable from eBay or Amazon, it will almost certainly use the Prolific PL-2303 or FTDI chipset. The software required to program the Motorola GP340