Martin,
From 2013 onward the default ServiceDesk Plus database has been changed to PostGres.
The application backup which you created from the MySql instance is compatible with the PostGres installation as well. The migration is handled by the application internally, it doesn't require a external conversion tool. Please restore the data in the new installation, it will work with it.
To restore a backup file, check the procedure in the link below.,
http://www.manageengine.com/products/service-desk/faq-general-modules.html#BackupRestore3
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SDP Support - FAQ
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SDP Support - FAQ
ServiceDesk Plus - Help Desk Software of your Choice