if they don't need a new printer, and if mom is happy with what she has.. don't fix what ain't broken (in mom's eyes). or just look for 3rd party ink for it. many and good reviews, reputable seller. it may take a couple tries to find some that work. hopefully mom hasn't allowed an hp firmware update that nixes that option and doesn't let you roll it back.

if you do replace the printer:

if they're low volume, can live without color, or are sporadic printer users, get a laser. a b/w brother with the features you want, that has 3rd party toners and drum kits available.

if they're higher volume and regular printer users (they don't not print for weeks or months at a time) and 'need' color, you could consider one of those 'tank-based' color inkjets. do not let it run out of ink and always leave it plugged in to the power (let it go into power-save on its own). they also usually have 3rd party ink available. you may want to see if and how the printheads themselves get replaced when needed and whether or not you can actually buy them (we're binning one here because the printer says it needs a new printhead---but you can't buy them!).

for photos, stick 'em on a flash drive and go to walmart or a drug store that has the self-service photo printing stations or use an online service that ships. it's much cheaper than printing photos at home.

read the box, and all its fine print. some printers (mostly, but not exclusively hp) are shipping with strict blocks on 3rd party consumables. hp had previously reserved the hardcore blocking to the first firmware update you'd get after setting it up (let that update come in, you were screwed. disabled firmware updates and you were 'ok')... but not anymore.

duplex printing (both sides, automatically) is something we use a lot. a sheet feeder (adf) on top for copies and scans is another feature we couldn't live without at the office. even though it might only be used occasionally--when it is needed, it saves so much time.

two other features that are often overlooked is a second input feed (even if it's 'manual'/one sheet at a time) for envelopes, letterhead or a sheet of labels.. and a main input tray with a decent capacity.. the one i'm using now only holds 50 sheets (about 30 in practice, because if you dare to fill it, it will misfeed frequently), and that's just not enough.

for printing from phones and tablets. look for that feature in the printer specs, then when you set it up at home, set it up as a wifi printer.