how to transform a photo into a puzzle

Yes.

1. Apply a filter to the photo that turns it to black and white, e.g. Color > Greyscale
2. Turn the photo into a patterned rectangle: Object > Pattern > Object to Pattern
3. Scale and move the pattern handles with the node tool, so the pattern fills the whole rectangle
3. Use a vector jigsaw to cut the patterned rectangle into pieces (e.g. one of these: https://openclipart.org/search/?query=jigsaw&page=2): Import jigsaw, ungroup (Ctrl+Shift+G), until the status line says it has only selected paths, combine the paths to one (Ctrl+K), select jigsaw and patterned rectangle, then do Path > Division. Depending on the jigsaw vector image, you may need to separate some of the pieces manually.