Can't find a compatible driver for a Brother HL-2240 USB printer

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Proceed with Great Caution as this may or may not work

Brother HL-2240 printer works with macOS … - Apple Community

It was suggested for macOS 12 Monterey that using the macOS 10.15 Catalina Driver may or may not work

There might be some other Third Party Software available to enable Printing with this computer

But, the printer is not listed as AirPrint compatible so than avenue is closed

Further, the Brother Site for Drivers appears to Ends with macOS 10.15 Catalina

I do know there are some very Knowledgeable Contributors who may " pop in " and offer some more concrete solutions but I am not one of them 😔

refer to below

It has been reported a few times here that the EU's consumer protection is more severe than here in the US and the are requiring manufacturers to provide drivers for the newer systems. You might try the European Brother websites to see if they have a Ventura compatible driver for you model.

If in the future you replace this printer, make sure you look for "AirPrint" support, so you never have to worry about the vendor discontinuing driver support for your printer.

Welcome

Time permitting, do keep us posted on the progress

Welcome and Thank you too

That is good news