i don’t disagree with the idea of having transfer or import/export functionality built within iNat, but i think these would be viewed as 2 separate things. there are some other conversations I’ve seen in the forum where folks talk about wanting to share observations, and that may sort of overlap with the idea of the “transfer” you’re looking for.
in the current system, the only way i know of to download stuff on the iNaturalist front-end (sort of) currently is to export observation data (as a CSV file), but it doesn’t come with photos, and the export only gives you the URL of one of the photos in your observation (if you have observations with multiple photos). but you could take the photo URLs from the CSV and modify them a bit to create a list of photos to download. then if you’re in Windows, you could probably do something described here (https://stackoverflow.com/questions/42878196/download-images-from-list-of-urls), using wget to pull photos into a folder on your machine. in Mac/Unix, it’s a little more complicated (see https://stackoverflow.com/questions/29551419/download-list-of-images-from-urls). one issue is that the photos that you download, i believe, will be stripped of the original photo metadata, if that’s important to you.
uploading things back on the existing front end would be challenging though. i’m pretty sure you could streamline that process with the API and a little bit of coding, though. you might be able to find some code that others have been working on to do that if you do a quick web search.