The Profile is juts a small file that allows the Beta to be installed. But the actual installer is only available from Apple directly though Software update.
Apple does not keep Beta archives, and since the only way to install a beta is through the software Update on the device, there's no way for anyone to install past betas.
Even if you could find a Beta install package, it won't install now since Apple stops signing older betas once the actual version is released.
Also, installed Betas expire after a while anyway and require installation of a newer Beta or the final release.
So installing old Betas is not something that can really be done.