With customers jumping ship to other smartphones, BlackBerry’s rescue mission could soon become a recovery operation. Pfizer (PFE), one of the world’s largest pharmaceutical companies, recently told its BlackBerry users to switch to an Apple iPhone or Google (GOOG) Android-based handset when their wireless contracts permit an upgrade, Bloomberg reported Thursday . Pfizer is concerned that BlackBerry might not be around in the future or that service could be interrupted, Bloomberg reported. Pfizer employs about 90,000 people, and its BlackBerry deployment is “sizable … huge,” AllThingsD reported . Meanwhile, the U.S. Department of Defense, owner of 470,000 BlackBerry (BBRY) handsets, is readying a contingency plan for moving away from the BlackBerry platform, NextGov reported Monday . For now, only BlackBerry devices are approved to operate on the Pentagon’s network. Once a favorite among corporate and government customers because of its secure email system, BlackBerry has seen its market share tumble as Apple ‘s (AAPL) …