Currently, PyDocTeur won't be able to detect the PR from a check_run or check_suite completed payload.
This is because of the github API:
Note: The Checks API only looks for pushes in the repository where the check suite or check run were created. Pushes to a branch in a forked repository are not detected and return an empty pull_requests array and a null value for head_branch.
https://developer.github.com/v3/checks/suites/