If you already own a property in another country, then you pay an additional rate of stamp duty in the house that you are buying in the UK. Unfair, but that’s how it is: https://www.primelocation.com/discover/buying/guide-to-the-3-stamp-duty-surcharge/#5GCwe4ErVlc2cLVE.97
You are also not classed as a first-time buyer.
If they don’t need a mortgage, there is no reason why they could not purchase the property in their own name but they already have a house, then once again they pay the additional rate of stamp duty.
Apart from stamp duty, there is no problem doing what you are proposing so I’m not altogether certain what the problem is that you are anticipating.
Can I clarify anything else for you?
I am happy to answer any specific points arising from this.
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