Webhooks contain a cryptographically signed token that is unique to a single repository with payload verification. It is therefore not possible to re-use the same webhook.
In your case, when the build starts, you can configure a step in your pipeline that launches a new build for your other project using the API or CLI. There is a third party plugin you can use that encapsulates this functionality. See https://github.com/UKHomeOffice/drone-trigger