Once you optimize the images on your website with ShortPixel Image Optimizer, they will remain optimized unless you choose to manually restore them. If you move your website to a new hosting, as long as you copy all the images and also the database, the images will remain optimized and you won’t have to re-optimize them.
One important detail to keep in mind is related to file ownership and permissions, which may be different on the new hosting provider. Please consult with your new hosting provider on how to make sure that your file ownership and permissions will remain the same.