Is it true by writing in 'paid in full' in the memo of a check and the check is cashed - the account is considered paid?
It can mean that. Usually you also need to provide some explanation with the paid in full check. For example a payment sending a partial payment for repairs done to an appliance stating that some of the repairs were faulty and as such the payment has been reduced by 25$ along with a "paid in full" check. If you are looking for more information you can use the internet to look up accord and severance which is the legal term for the process.
From Byron Petersen:
It is not true.
In the past special language could be put on the back of the check at the endorsement section, but even that has changed.
Byron Petersen