Hi Isaac,
The found male is clearly a tame bird, and with a tame bird, it is best not to put another bird in the same cage. While they are not getting along now, they may eventually bond and lose interest in being pets. New birds should not just be put in a cage with each other. You know nothing about this found bird. If the female is under 2 years old, she should not be in a cage with a male. It can cause her to try to lay eggs while she is too young, which can result in egg binding, which can be fatal. I would split the birds up for now. When introducing two birds, you put them in cages side by side, so they can get used to each other. But before this, both birds should be taken to an Avian Vet for a check up. Since the male was found outside, he could have gotten internal or external parasites from wild birds. There are also diseases that cockatiels can carry – one being Chlamydiosis which humans can get. Cockatiels should always be tested for this and other diseases, especially when you know nothing about their background. One both birds have a clean bill of health, they can get to know each other by being in cages side by side. When they do show interest in one another, then you introduce them gradually and only if you supervise them closely. Again, if you want the male to remain tame and be able to handle him, it is best to take the female back to the store. A pet bird doesn’t need a bird companion because you want it to be tame to humans, not bonded with another bird.
Thank you for asking Lafeber,
Brenda