There's 2 subjects entangled so far?
1. If an Aust. citizen is appoved for the OAP, can they receive the 4 weekty payments (full OAP entitlement and OAP supplement) in Thailand on a very long-term basis (lifetime)? The basic answer is yes if that person is entitled to 'portability'.
But when abroad the pensioner is not entitled to the energy allowance or rent ssistance.
If paid abroad the payments change from fortnightly to 4 weekly ( 2 fortnights). Transeffered by international bank transfer from Service Autralia (Centrelink) to the bank account of the recipient in the country abroad. e.g. K Bank of BBL, or....
The bank fees ae tiny and the transfer is very fast. The name of the bank account to receive the funds must include the name of the persioner, but it can be a joint savings account, the pensioner and one more person. Centrelink prefer that the second name on the bank account to be a family member but that's not compulsory. Cenrelink is not interested in any details re who must sign for withrawal in the other country. Can be the pensioner alone, or the second account owner alone or both parties. Up to you.
Mine is a K Bank joint savings account, myself and my Thai son (I was not asked for any proof he is my son). As soon as the funds are deposited I get an instantaneous e.mailed 'Credit Advice' from K Bank in English and in Thai. I had to request this facility, took 5 minutes, it's not free, from memory 200Baht per year.
2. Australian taxation implications when the OAP is being received abroad - already much written in these threads on that point. And difficult to find a clear answer. If the OAP is the only income then it's likely there's no tax implications.