Brother mobile connect app won’t print documents

Two printers (Brother DCP-L2640DN and Brother DCP-L2640DW) are listed as supported in the AirPrint article mentioned by LD150. If you have one of these exact models, you should be able to print from an iPhone 16 without additional apps, provided that the printer and the iPhone are connected to the same network (Wi-Fi router). A DN model would have to be wired (Ethernet) to a LAN port of the Wi-Fi router, whereas the DW model appears to offer a choice between a wired and wireless printer connection to the router.

Use AirPrint to print from your iPhone or iPad - Apple Support

About AirPrint – Apple Support (UK)

Your printer does not seem to be an airprinter, otherwise you would not need the app. Contact Brother, see if there is an update to the app, but these apps generally are useless.