Yes, just get a PAC code by text for the number and give that to whoever you're going SIM only with. That would be the way of doing it even if you are staying with VM, because from the company's point of view it's your mum ending her contract and leaving, and you're a new customer joining.
Bear in mind that currently the number is probably supported by the EE network, the new SIM only deal will be on Vodafone if you stay with VM, and in the next few years that may well transition to O2, so check for any coverage issues that matter to you.
In your shoes I'd be looking at newer providers who don't have legacy call centre business models, so people like giggaff, smarty, Tesco Mobile, ID Mobile because their on line account management will be better, but again check who provides the physical network in case that affects your coverage. And finally, it usually makes more sense to have 30 day rolling SIM only contracts, and avoids lengthy lock-ins. Long SIM only contracts are a touch cheaper, but that's no good if the mast near your house is decommissioned and the new arrangement has worse signal, or if your circumstances change and you move somewhere where there's only coverage from another network.
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You might find this helpful, on Martin Lewis’ website when searching for a mobile deal, the filter option lists the main networks with a list under each of who uses them. It’s accurate for new contracts or sign ups. The list will appear here once it’s been checked!