What era/country/manufacture is this vintage step through?
This may not be the info you expect, but for your purposes, it doesn't matter at all.
Your mother wants to ride again, and that's fantastically awesome.  Anything that progresses the goal nearer to completion is good.
I suggest you find out if she had a bike in the past, what brand it was, what colour, and anything she remembers about it.  Perhaps conscript any other family to ask on your behalf so its a surprise.
Then paint the bike that colour, or fit a basket if she remembers having one.  Fit an Ahhooga horn if she remembers that.
Buy or make a set of decals that say the same brand as she had, or make ones that say her preferred name,  or even MOM'S BIKE or BLIC for bucket list item completed
You're doing a great job, keep it up.