You can never arrive at an exact answer - you can only guess at how your friend chooses the coin, and then see how likely your guess is to be true.
You might make the hypothesis that your friend always chose coin $B$. In that case, the probability of getting a head would be $0.5$ - you might not think that was likely enough, but most hypotheses are rejected only when they predict that the observed behaviour will occur with probability at most $0.1$.
You might suppose that your friend chooses the coins at random. In that case, the probability of getting a head would be $0.75$ - that seems likely enough.
The fact that the coin landed heads is, unfortunately, not enough to tell you anything about how your friend had chosen the coin. If it had landed on tails, then you would know that your friend had chosen $B$, and you would know that she had not adopted the strategy 'always choose heads', and you could be reasonably confident that she had not adopted the strategy 'choose heads with probability $0.99$; otherwise, choose tails'. Of course, in that case, you would know that your friend had chosen $B$, but...
So you really have nothing to work with. What you need to do is to repeat the process a number of times, assuming that your friend uses the same strategy each time.
Suppose we wish to test the hypothesis that your friend chooses the coin randomly with probability $\frac{1}{2}$. Get your friend to toss the coin $10000$ times. Now we define the $95\%$ confidence interval for the number of heads under our hypothesis to be a range of values for the number of heads such that if our hypothesis is correct, there is a $0.95$ chance that the number of heads lies in that range. A quick calculation (details of which I am happy to provide) shows that this interval is [7415,7585]. So if your friend tosses $7503$ heads, you can be reasonable confident in your hypothesis. However, if she tosses $8703$, then you are probably wrong.
Suppose you have good reason to believe that your friend is choosing the coins randomly with probability $\frac{1}{2}$, and you observe her toss $7503$ out of $1000$ heads. Then you have no evidence to reject your hypothesis, so you accept it. Now suppose your friend tosses again and gets a head. Using Emile's method, you know the probability she chose coin $A$ is $\frac{1}{3}$.