Using stock image *for* a client project vs. the client using it themselves

Hi all,

I purchased and used a stock image as the basis for my client's social media graphics last year. This week they approached me asking if they could use the same image themselves for creating website graphics.

If I understand licensing and usage rights correctly, I would be able to make those web graphics myself since I purchased the original image, but I'm unclear on what it means that they want to make the new graphic(s) themselves.

Does my purchasing the image cover them, since it's the same client the image was originally purchased for? Or would they need to buy the image themselves since they'd be using it without my involvement?

Thanks ahead of time.