Before moving them, you need to make sure the new tank is cycled. There are a few ways to do this and there are articles on the site(I'd post them here but I'm on my phone). Once that is done, transferring should be easy.
Be warned, not all betta like tankmates. It depends on their personality. It seems like you have not had any issues so far, but a fishes personality could always change, especially if your moving him to a new tank. Some say put the tetra in first for a day so they are there before the betta gets there for territory reasons.
As mentioned above, bigger is usually better, however you could keep the betta in the 4.5g. I have mine by himself in a 5 with live plants and he loves it. Then you could try to add more with the tetra in the 65l. either way, make sure the tank is cycled.