Test takers' certificates are set to private by default. In order for test takers to share their certificate publicly (including when they take a screenshot or make a PDF of their certificate), they will need to set their certificate to public/shareable. They can do this by logging into their Duolingo English Test account, clicking the "Certificate" button next to their result,, and then clicking the "Get Shareable Link" button. This makes their certificate public, and it makes the URL link appear on the certificate.
Note that when a test taker shares their result with your institutional dashboard through the Duolingo English Test website, which is the sole official way to share their result, you will be able to see their verified certificate URL link on your dashboard.
If test takers are being asked upload a screenshot or PDF of their certificates to an admissions system, you may not see certificate links on some of them. In these situations, please ask the test takers to send their results officially through the Duolingo English Test website (which would allow you to log into your account to verify the result), or ask the test takers to make their certificate link shareable before they make a PDF, so the URL will appear on the image.