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The LiMux wiki page mentions a timeline of how the migration happened, so it looks like their phased rollout helped them 'convert' to Linux smoothly.

Quoting from the wiki.. September 6, 2005 - It is decided that the project needs an additional one year pilot test, and migration slips one year.[19]

September 22, 2006 - The "soft" migration begins, one year behind original schedule.[20]

November 2008: 1200 out of 14,000 have migrated to the LiMux environment (9%; March 2008: 1000=7%), in addition 12000 workstations use OpenOffice.org 2 installed on Windows (March 2008: 6000) and more 100% use Mozilla Firefox 1.5 and Mozilla Thunderbird 1.5 (March 2008: 90%). 18000 of 21000 macros, templates and forms are changed into Linux-enabled[21]