Hm, I have actually done the same on our own site this morning (also hosted on SiteGround) and everything worked. Just to make sure, what you should do to install this beta version is:
- Go to our download page and download the ZIP package
- Log in to your site
- Go to Extensions, Manage, Install and upload the ZIP package
Why do that? Since this is a beta release, the default Joomla! settings will prevent automatic updates through Extensions, Manage. If you want to enable installation of beta releases please go to Extensions, Manage and click on Options. Set the Minimum Stability to Beta and click on Save & Close. Click on Update, Clear Cache and when it finishes click on Find Updates. Now 4.4.2.b1 should be directly installable as an update.
FYI the minimum stability feature in the Joomla! extensions updater was added in Joomla! 3.4 and was submitted by yours truly :)
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
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