Convert Screenshot to 300 DPI PDF

I have a single screenshot—format unknown at the moment—that I need turned into a print-ready PDF at a true 300 DPI. The file will be sent to a packaging supplier to be printed on a custom box, so clarity is critical. Please keep the image’s proportions intact unless a minor adjustment would improve print quality, and feel free to apply light enhancement or sharpening if it helps the final result look crisp.

Deliverable:
• One PDF, 300 DPI, ready for professional printing on the box

Let me know what file type you prefer me to supply and how quickly you can turn this around.