A study that was conducted in 1991 called Post-exercise net protein synthesis in human muscle from orally administered amino acids provides exciting information that you can apply in your daily training routine.
A group of professional scientists examined the benefits of BCAAs supplementation both prior and after training.
In the first study, they examined six healthy adults, three women, and three men, consuming BCAA supplementation after training. The immediate effect of producing muscle protein growth was effective with the individuals who consumed BCAA supplementation compared to those who didn’t (placebo).
Another study called Timing of amino acid-carbohydrate ingestion alters anabolic response of muscle to resistance exercise examined a different protocol, with the individuals to consume BCCA supplementation before training with simple sugar.
They reported that when BCAAs are digested 30 minutes before training with simple sugar, the anabolic response in their muscle was much greater compared to consuming after training.
Ultimately, the decision is yours to see what is most effective for you. You have to do what is best for you and when you feel it is best. The research here provides information, and it does not apply to everyone.