Extract a custom painting from one lot and add it to another, including all necessary linkages:
http://www.modthesims.info/showthread.php?t=491281

This should be another fairly simple program, assuming that the painting image still exists in the lot package after the painting has been moved to another lot.

Research required: what linkages are necessary? Are the linkages still intact, even though the image has been removed?

References:
http://www.modthesims.info/showthread.php?t=455728
http://www.modthesims.info/showthread.php?t=391825

[Update:] I just had my sim take a custom painting and a still life to an owned business lot and the pictures showed up correctly. I also verified that the paintings are in the business lot package, not the residential lot package. Is this only a problem with some EPs?

This would be great. I've lost some paintings I really liked.

I know that one of them was lost moving from residential to residential lot.

If you still have a backup of the original lot before the move occurred, you might be able to grab the picture from the lot package.