Welcome to the forum!
It's not about who owns the image. It's about Inkscape knowing where it is. If you imported it into Inkscape, and later you decided to put that image in a different folder, well now, Inkscape doesn't know where it is. It can't find it. When you were working with someone else's image, it might have even been on a whole other computer. There are 2 possible solutions.
When you first import the image, there's a little dialog which comes up, which you might just click through without looking. But it asks if you want to link it or embed it. If you see the "Linked Image Not Found" that means it's linked. You could switch to embedding, and that would make it always available, no matter where you might take that SVG file later (or no matter where you might take the original raster image).
There is a caveat with embedding, and that is that it only takes a handful of imported raster images before you start to see performance issues with Inkscape. The embedded raster images swell up the file size pretty fast. As far as I understand, the more RAM you have, the more raster images you can embed, before the performance issues start. You can only experiment to learn how many works best for you. There's not really any kind of optimal number.
Or the other solution, is to link it, and remember not to move the original image after you import it.
Edit
Rather than importing it again, to be able to switch to embedded, you can select it, and then use Extensions menu > Images > Embed Images....
