You need to install the latest version of REBUG CFW on your PS3.
Then, after that, install "
psnpatch". With it, you will be able to hide the CFW functions and access the PSN Store in a more safe way (avoiding a possible block/ban from $ony).
With that all set, run psnpatch, access the PSN store and download what you want.
Then, on the Vita and PC, in PC, use VitaUpdateBlocker 1.2 has a proxy to block the update request for the Vita.
On the Vita, configure the proxy, and connect your Vita to the PS3 to transfer the game from the PS3 to the Vita.
I'm not sure if the PS3 needs to be connected to the Internet to transfer the content from the PS3 to the Vita. Try it without Internet, if it needs it, connect the internet, but make sure to run the psnpatch to patch the CFW functions, just to be safe.
So remember, keypoints:
PS3:
- REBUG latest firmware
- PSNPatch (hide CFW functions)
PC:
- VitaUpdateBlocker (use as proxy)
Vita:
- Configure Proxy settings
I guess that's all you need, IIRC.