If you're on Exchange 2010 SP1, you could enable Internet Calendar Sharing and publish
User B's calendar in iCalendar format for
User A to pick up.
This Microsoft Exchange Team Blog post goes into detail on the subject, though it's a bit wordy and mixed in with some other cloud-peddling bumph. Probably the most relevant bullet point to you is this one:
- Internet Calendar Sharing allows users to share (and subscribe to) calendar data in iCalendar format with any anybody, inside or outside the organization, whether those recipients are using Exchange, another platform, or simply a web browser. Internet Calendar Sharing does not require authenticated access or Federated Trust, and the only setup required is for the Exchange administrator to turn the feature on.
The Enable Internet Calendar Publishing notes on TechNet go through the process which is basically enabling the feature with a couple of cmdlets, creating a sharing policy and assigning it to mailboxes.
To actually share the calendar,
User B can use either Outlook 2010 or OWA (instructions), or you as the administrator can use PowerShell to publish a calendar for the user.