You don't tell anything about the system configuration at User B's work. But let's assume they have Exchange Server or Lotus Notes. Then anyone with administrative privileges (say, the system manager) would be able to read any mail on the system, I think, maybe even (unknowingly) generate a read receipt when opening it.
Let user B contact his 'postmaster' for information.

Juridical aspects are interesting. Can an employer rightfully open a private looking e-mail (sender and subject might tell a lot)? Is an employer allowed to read a e-mail that's clearly business? I'm inclined to say 'yes' to the second question, and 'yes, if ...' to the first. The 'if' however is important. It should be clear that private e-mail is not allowed at work, and here in Holland the 'council of employers' must have agreed with the exact regulations and conditions for spying.
But, of course, the USA is not Holland. If the mail has a subject linking it to terrorism, I think much more is allowed nowadays in the USA.