Sony is looking at the possibility of how to do it
Sony is apparently again considering a conversion program for PSP owners with UMD titles for its Vita platform. Previously, the company looked at offering such a program for the PSPGo, but in the end decided that the logistics and cost were just too much.
Since the PSP games that were originally released on UMD, but later made available in the PSN store in digital form, are compatible with the Vita it presents an interesting option for Sony to make a big splash and reason for users to upgrade from the PSP to the Vita.
While Sony is looking at this challenge and trying to find a solution that will work for both the consumer and the company, no plans have been confirmed yet. It is likely, however, that the program would be restricted to the oldest UMD releases and the UMDs would have to be exchanged for the download versions, which would likely come as a download code of some sort.
Hard to say if Sony can sort this out and make it work, but if they can it could be just the shot in the arm that the Vita needs to get it off and running.