according to the documentation the upgrade path from Sitefinity 4.4 is:
4.4 » 5.0 » 5.2 » 5.4 » 6.1
You can download the project manager for each version by logging into your Sitefinity.com account to download the Sitefinity installer, but instead of the latest look for a link that says "Older versions".
Choose the most recent version of each major release, and be sure to download the ZIP of the Project Manager, not the installer.
I hope this is helpful!