What the speaker is trying to do in A is emphasize "she liked it."
The it is probably technically ungrammatical if this is really meant as one single phrase.
The "thing" that "she liked" is the entire phrase "that her friends boasted about her.* So specifying an object it for liked is redundant and unclear - it would normally refer to a noun, but even if it didn't, you wouldn't use it to refer to a phrase and then specify the phrase. That's like saying "Give the money to her my mom."
Now, if two phrases are meant, it's OK:
She liked it, that her friends boasted about her.
In speaking this, there would be a noticeable pause or lowering of voice pitch (similar to that at the end of a sentence) between it and that.
Give the money to her, my mom
is also OK.
I think, but am not sure, that these are examples of appositive construction.