Hi @esguicero,
For an update from a vintage version of Specify (over 10 years old), we usually ask that you send us a copy of the database so we can update it and prevent issues during the upgrade process. Please note that we can only provide this server to members of the Specify Collections Consortium.
We provide current installers for Specify 6 releases back to 6.7.00, but you can download the Specify 6.6 releases on the Internet Archive.
You’ll need to step through each version, from 6.6.00 → 6.6.06, before updating to 6.7.00 and stepping through each version until you get to 6.8.03.