Ask the program officer (PO), because he/she will be able to back you up if the permission comes from him/her, should the reviewers criticize so.
However, slightly recast your question. For instance, ask if the proposal will be reviewed with your previous proposal side by side or by the same reviewers. Tell the PO that you ask because you intended to frame the background with some similar information you presented in the last version, but worried that it would create redundancy. And emphasize that you will be more than happy to transfer the background to the continual application if that would make the application process smoother.
In the mean time, evaluate the magnitude of the intended cutting and pasting and what information is being transferred. Historical findings are unlikely to change and can understandably be worded similarly; but if what you want to paste were things that you would set off to explain/learn, and after three years the unknowns remain, then it probably will not go too well. Also, critically review the literature. If the parts to be cut and pasted are more contemporary literature review, it's hard to believe nothing can be added in three years. Anyway, don't use them just because you don't have time to revise the background and the last one seems still pretty good.