How can I subclone the shRNA and GFP marker out of pGIPZ and into another vector of my choice?
That depends on whether you want to also take the CMV promoter with the TurboGFP and the shRNA. If you are willing to take the CMV promoter as well, a simple XbaI/MluI should work. We have not done this in-house, so we cannot guarantee it to work.
We would not recommend using XbaI/EcoRI since two of the bands will be only 78bp apart and one of those would be the one you need (there are two EcoRI sites in the pGIPZ vector).
If you do not want the CMV promoter then the only way to get an insert with TurboGFP and the shRNA is to PCR amplify it.