The current (2017) chronology of the IP and licenses is:
1989 - FASA corporation creates Shadowrun.
1989 - Beam Software acquires the license for one SNES title. 1993 it publishes the game under the title Shadowrun.
before 1990 - FanPro GmbH acquires the German Shadowrun license.
before 1993 - BlueSky Software works on a SEGA Genesis title, published as Shadowrun in 1994.
before 1995 - Compile Co. Ltd works on a SEGA Mega-CD title, published as Shadowrun in 1996 as the last Mega-CD title ever
2001 - FASA closes doors as a publisher and becomes an IP holder. The Shadowrun IP is bought by WizKids LLC. Shortly after FanPro LLC is founded by FanPro GmbH and gains a whole bundle of licenses from WizKids, including Shadowrun.
2003 - WizKids and its held IP are bought by Topps, but still controls handing out its licenses as a subsidiary.
ca. 2004 - Microsoft trademarks Shadowrun for PC & X-Box after acquiring the license. FASA Studio produces under this license the FPS "Shadowrun" to be published in 2007.
2006/7 - Fast Forward Enterprises (FanPro GmbH's warehouse and shipping partner) goes bancrupt. As it vanishes with a lot of funds from FanPro GmbH, it has in turn has to siphon funds from FanPro LLC. Over the months this becomes unsupportable, and starting April 2007 FanPro GmbH sells off the IP & licenses they own (for example the Dark Eye, but not Shadowrun) in a pitch to raise enough money to stay afloat.
February-April 2007 - WizKids doesn't renew the bundle of licenses FanPro LLC and FanPro GmbH held, but negotiated with InMediaRes Productions LLC. Only the german Shadowrun novel license remains at FanPro GmbH, the rest returns to WizKids/Topps.
May 2007 - IMR founds Catalys Games LabsLLC (CGL) to hold the tabletop licenses and shortly after sublicenses the German Shadowrun tabletop license to Pegasus Spiele GmbH (often referenced as Pegasus Press).
2008 - FanPro GmbH stops publishing the German Shadowrun novels over a dispute if they had retained the license or not.
2008 - Topps announces to close WizKids, retaining some IP (like Shadowrun) while selling the rest of WizKids (like HeroClix) to National Entertainment Collectibles Association in September 2009. CGL (for IMR) retains the Shadowrun tabletop licenses, as does Pegasus.
Early 2012 - Harebrained Schemes acquires the Computer license from CGL & Topps, payed via Kickstarter, making with it the Shadowrun Returns series.
July 2012 - Cliffhanger Productions acquires the mobile & online license from Microsoft, CGL & Topps via crowdfunding. The game originally planned as Shadowrun Online is published as Shadowrun Chronicles: Boston Lockdown in 2015.