Bob is a boy. Alice is [a/the] boy's friend.
There is a dilemma to me: I know that the should be used to specify a specific boy (Bob), but at the same, should a be used there to be applied to friend to convey that friend is a noun?
P.S. I've read this and it says that a possessive does not cancel the requirement to use articles, so the question remains.
The correct article depends on the actual situation.
If you mean to explicitly say that Alice is Bob's friend, you would use the definite article:
Bob is a boy. Alice is the boy's friend.
But, even better, don't use an article at all:
Bob is a boy. Alice is Bob's friend.
Bob is a boy. Alice is his friend.
On the other hand, if you mean to say that Alice is the friend of a boy who is not Bob, then you would say:
Bob is a boy. Alice is another boy's friend.
Bob is a boy. Alice is a different boy's friend.
❔ Bob is a boy. Alice is a boy's friend.
If you use the indefinite article, the interpretation of who Alice is a friend of is ambiguous. It's not obvious if she's Bob's friend or somebody else's friend.
The article "a" is indefinite, meaning it is not specific.
Alice is a boy's friend.
Is a perfectly good sentence, but we know nothing about "boy" other than there is one out there somewhere who is Alice's friend. It could be any boy, anywhere.
The article "the" is definite, meaning it is specific.
Alice is the boy's friend.
This tells us there there is a specific boy out there somewhere who is Alice's friend. Not just any boy, but a specific boy.
In your full example, you would use "the" because Bob was introduced and (we presume) the goal is to identify Bob as Alice's friend.
Bob is a boy. Alice is the boy's friend.
