Getting job artifacts API always returns 404 when the pipeline is triggered by different upstream pipelines

I have a downstream pipeline in a separate project which stores some data in a job artifact. I use the $CI_API_V4_URL/projects/$CI_PROJECT_ID/jobs/artifacts/main/download?job=job API to get artifacts from the last successful build in the downstream project. But it works ONLY when I trigger the pipeline from within the downstream project. When this pipeline is triggered by an external project, the API always returns 404 while I have a lot of previous successful downstream pipelines with artifacts. But I need to get exactly what documentation says: an artifact from the last successful pipeline in the project. Upstream projects don't have jobs with the same name.

How to fix that?