Seriously this lasting power of attorney LPA needs challenging by your usual Solicitor, this was not drawn up correctly in line with regulations through the OPG (office public guardian) when a LPA is granted then the Three next of kin should be notified when the power is about to be registered with the http://www.publicguardian.gov.uk/arrangements/lpa.htm without this procedure being strictly followed, the LPA can be revoked by the OPG.
This would mean that when your Father made the last will that he was quite possibly testamentary incapable of making it, therefore this will could be challenged as to it's validity and remade by the courts or his old will re-instated so that only his children benefit from it. !
The actions of this inexperienced Solicitor need very close investigation for neglect or other more sinister concerns that he stands to benefit himself along with "another person" in collusion, at the worst legal action could be pursued to recover all losses and sue him for damages caused by his duty to act in his clients best interests.
From what I understand at this moment your Father was (legally mugged) or very nearly, if things go left unchallenged.
You need to see an experienced Solicitor IMHO about the whole charade.
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How can I make an offer on it anonymously? How would proxy purchase work, or should we set up a company? Or is there a simpler way of the executor transferring title and ensuring the 3rd. person receives 1/3 the value?
To answer that part of your question ...the Solicitor will always know the identity of the purchaser, he has to in order to comply with money laundering regulations even if it was a company the directors identity(s) would be recorded and checkable.