Research In Motion shares climbed in early trading Friday after a Jefferies & Co. analyst upgraded the BlackBerry maker’s stock to “Buy,” citing the potential for its new software to offer corporate e-mail on rival devices.

RIM (Nasdaq: RIMM) rose as much as 7.6 percent to $16.05 today, after Peter Misek, a Jefferies’s analyst, said the company may be able to retain more corporate customers because its new BlackBerry 10 secure e-mail will be available on devices that run Apple Inc. iOS and Google Inc.’s Android software.

The shares had gained 1.2 percent in New York on Thursday.

RIM’s value has more than doubled since late September amid growing investor optimism that the new BlackBerry 10 software set to debut Jan. 30 can engineer a sales recovery and return to profit. Earlier this week, the Waterloo, Ontario-based company said more than 1,600 companies in North America have signed up to test out BlackBerry 10, reflecting business users’ enthusiasm to try the new phones.

The fact that BlackBerry 10 will offer companies the option of offering secure BlackBerry e-mail service on rival devices is “unknown or not well understood,” Misek wrote in the note, where he lifted his rating from hold for the first time since April 2011. He also raised his price target on RIM to $19.50 from $13.

Investors could win if “RIM creates a successful software business on top of Android/iOS,” he wrote.

Apple’s and Google’s operating systems are the main reason RIM has lost so much market share in recent years. RIM was poised to finish 2012 with a 4.7 percent share of the global market, compared with almost 90 percent for Apple and Android combined, research firm IDC said last month.

RIM operates a research and development office in the Research Triangle Park, N.C. area.