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As I am sure you are aware, as Executor, it is your duty and only your duty, to decide what happens to the property. It would of course be normal for the property to be sold.
However, provided the beneficiary is able to pay the true market value for the property, there is no reason why a Sale to him/her can not proceed.
I am not sure why the beneficiary has taken it upon themselves to get valuations etc, and if you do proceed with a Sale to them, you will have to disregard any valuation the beneficiary has already obtained. You will of course need to be impartial and it would be normal for an Executor to obtain 3 valuations, and then choose the middle valuation as the Sale price of the property. If the beneficiary is prepared to proceed with this middle valuation, you are free to proceed, without any possible comeback from the other beneficiaries- indeed, you can also tell them that doing it this way, the Estate will be saved from having to pay Estate Agents commission, which is likely to be 1%-1.5% of the Sale price.
I hope this clarifies matters and sets out the legal position.