I don't see the need for an approved printer. It's going to print simple text. No formatting. Prints each line as it gets it. Right ? You're using as a logging / alarm printer ?
Here's a list of things I would do to set up a serial printer to a HMI. In general, it's how you would setup any two serial devices.
1. Setup printer: Tell it (via dip switch / menu ?) to use the serial port vs parr. port. Baud rate, stop bits, parity, handshake settings. Some printers default to parr. if a parr. cable is plug in. RTFM.
2. Setup HMI to use serial port: Enable it for function needed (Alarm log ?) Baud rate, stop bits, parity,handshake settings. RTFM.
3. Connect devices. See which pin is XMIT, RCV on each. Connect XMIT -> RCV. Sig Return connected together.
Check each device to see if any pins need jumpering. Like CTS to RTS, DTR to RTS. Most devices can operate in 3 wire (XMIT,RCV, SIG RTN) mode, some need actual pins jumpered, some can be set in configuration to no handshaking.
That's it. Where's the problem ?