Install an older iOS beta prerelease My phone was running iOS 9 beta 3 last night when my last backup happened. Today Apple gave me a new phone but when I got home I realized that my version of iOS is iOS 9 beta 4 and my backup will not restaure... Argh.

How can I get iOS 9 beta 3 on this new phone?
You can always restore a backup of an older version of iOS onto a newer version of iOS, just not vice versa.

If you really want to install an older pre-release version of iOS, then you can if you still have the IPSW. Apple doesn't stop signing pre-release versions like this so you should still be able to install an older version through iTunes.