By NICK WINGFIELD Microsoft Corp. has reached an agreement with Nokia Corp. to make a mobile version of Microsoft's Office suite of software that works on Nokia cellphones, according to a person familiar with the matter. The deal with Nokia, the world's biggest maker of mobile phones, could help Microsoft play a broader role in mobile devices while fortifying its Office business in the face of competition from free Web-based word processors, spreadsheets and other applications from Google Inc., Sun Microsystems Inc. and others. Microsoft, too, is testing a Web-based version of Office. The alliance between Nokia and Microsoft is another sign that the two companies, once fiercest competitors, are coming closer together as other mutual threats have emerged. Microsoft makes an operating system for cellphones called Windows Mobile that competes with Symbian, the software that powers most Nokia phones.