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A complete proof can be found in the first few pages of

https://mathscinet.ams.org/mathscinet-getitem?mr=977759

Jensen, Christian U.(DK-CPNH); Yui, Noriko(3-TRNT) Quaternion extensions. Algebraic geometry and commutative algebra, Vol. I, 155–182, Kinokuniya, Tokyo, 1988.

I will scan the relevant pages and post them here as soon as electricity is restored in my office.

Addendum: Here is the paper :

https://drive.google.com/open?id=0B8EHtI8F9qdIODNpZTQ1c1JjQTlIUUdsWm1nZmxRWVNTM1Bj