How to handle student plagiarism appropriately?
Usually, the way to handle this is to ask both students to come in at the same time. And then in separate rooms, ask them to articulate one of the key points of the essay. It's usually simple to determine who wrote the paper and understood the ideas and who merely copied the text.

However, the key issue doesn't seem to be just whether B copied from A, but whether:


A allowed B to copy the material willingly (perhaps for remuneration)
A allowed it to be copied by B accidentally or through neglect (e.g., A left a draft on a public computer); or, 
B copied it by malicious action  (B hacked into A's computer).


(There is a fourth possibility: that both B and A used source C and both are plagiarists.)

It would be unfair to punish just B and let A go without proving A's innocence or culpability.

That all being said, untangling this is non-trivial and at this point, I'd declare it above my pay grade and send it up the chain of command to the university committee responsible for student ethics and misconduct (via the instructor on record if you're a teaching assistant).