A DAW would be the way to go, and some DAWs are easier to use than others. If you can get her set up and show her how to record her keyboard in the DAW, then hopefully she'll be able to do it by herself the next time. But you'll want to know how to use the DAW yourself before you try to show her, so hopefully either you both use the same operating system and can use the same DAW, or else you can choose a DAW that's available on both of your operating systems.
PreSonus Studio One has a free edition called Studio One Prime, and it's available for Windows, macOS, and Linux. It won't let you record SysEx messages in the MIDI, and it does require a little bit of setting up as far as MIDI devices, but it's pretty easy to use once you've got things set up.
Tracktion has a free older version of their DAW-- which is called Tracktion, since the newer versions (called Waveform) aren't available for free yet-- and it is also available for Windows, macOS, and Linux. Unlike Studio One, Tracktion does let you record SysEx messages, but to me it seems a little bit harder to learn than Studio One.
Avid Pro Tools has a free edition called Pro Tools First, but I find it to be very complicated; the reference manual is over 1300 pages long, which is never a good sign-- unless you're looking for a DAW that's so advanced and feature-rich that it takes over 1300 pages to explain.
There's also Cakewalk by BandLab, although I haven't tried it yet.
As far as DAWs for Windows, my personal favorite as far as ease of use is Acoustica Mixcraft, but it doesn't have a free edition. It also doesn't let you record SysEx messages.