Seniors

You left out the "adverse" part of adverse possession. If someone allows you to stay on their property, you cannot gain title through adverse possession.

"claimed that years ago, the owner gave his word — but nothing in writing — allowing him to live there"

Here is the complete definition, and other particulars about New Hampshire:

https://courts-state-nh-us.libguides.com/adversepossession

"The elements of adverse possession are: the use must be adverse (without permission and hostile to the owner's interests); it must be notorious (the owner has had notice of the use); it must be continuous and uninterrupted; it must be exclusive (not in common with neighbors, or others), and it must be for a period of at least 20 years as defined in the statute of limitations for the recovery of real property (see RSA 508:2, I)."

His admission that the owner allowed him to live there defeats any claim to adverse possession.