The Vita's security restrictions (specifically its Content Manager Assistant-based PS3 transfer) don't support direct transfer of save data from within the game, but even copying the file onto a PC via USB drive, then transferring to Vita with the CMA program didn't work for Julius.
Since the Vita HD Collection doesn't include Peace Walker, "Transfarring" is effectively out of the picture on that platform. Ironic since many Vita games support Vita/PS3 connectivity under a different name.
This, of course, isn't even the biggest problem with playing Peace Walker on a Vita. The biggest problem, for those of us in North America, is that it's not even available through the Vita PlayStation Store. You can move it over if you bought it already, or you can buy it through the PS3, but you can't just buy it from the device you want to play it on.
Sony PlayStation 3 (late 2012)
Sony PlayStation Portable PSP-2000