"The letter was sent to OP - not directly addressed to her but sent to the house for the people currently living there and asking them to forward the enclosed letter as the sender knows the believed father no longer lives there but, presumably, has no knowledge of his new location and hopes current owners have a forwarding address."
Unless I've missed a post, OP has not said that the letter was "sent to the house for the people currently living there and asking them to forward the enclosed letter as the sender knows the believed father no longer lives there".
All she has said is that a signed for letter (which she had not signed for) had been put through the letter box.
That the envelope bore the house address but had no name on it; that the letter inside was addressed to the previous owner; that the letter contained no contact details for the sender. That the author asked the [previous occupant] to reach out to them.
So I don't know where you've understood the author of the letter was asking the current residents to forward the enclosed letter from - unless I've missed one of OP's posts.
If it were me, I would not attempt to locate the previous owner, I would not approach the conveyancing solicitor or estate agent to ask them if they would be prepared to forward an already opened letter that has no name on the envelope. OP could tuck the letter away, do nothing and see if any more letters arrive.
It still strikes me as peculiar that someone would go to the trouble and expense of paying for a letter to be sent as "signed for", but omitting the recipient's name from the envelope and omitting their own contact details.
An elaborate phishing operation? Malicious intent? Genuine, but wanting to let the man and his family know, but not making it easy for him to respond? Who knows?
I think we all love a mystery, but this is not something I would want to make myself a third party to.
And if OP did send it on, the previous owner will know that you and others in your family will have read the content of the letter - a situation, if genuine, that could potentially have explosive implications for him and his family and their financial plans.