If by wirelessly you mean via Wi-Fi network then one convenient option is qrcp. It generates a QR-code right in your terminal, which you can scan with a phone and send/receive files through a web interface on the URL it provides.
If you want to transfer files regularly, there is another option. Almost every distro has Python installed, and the Python has a "built-in" FTP server.
You need to just cd into desired directory and run the command python -m pyftpdlib -w. It will open a FTP server with root in this directory.
You then can access it through a file manager, like Material Files for example, and send files and folders back and forth. In Material Files you can save the server address for future use.
I know that habit of using messenger app for notes :) Try [matrix] using Element or SchildiChat. It's e2eencrypted and federated, and even supports markdown formatting in messages. Also some Slack features are included. The only issue for non-techy person might be verifying sessions - just be sure to use the same client on all devices.