After moving Service Desk issue, email comes in at original (closed) issue

Summary

After moving a Service Desk issue to another project, new email sent to the incoming+...@incoming.gitlab.com address will still come in at the original (closed) issue instead of the newly created (moved) issue.

ZD: https://gitlab.zendesk.com/agent/tickets/119876 (internal)

Steps to reproduce

1. Send an email to the Service Desk's incoming email address; this opens a SD issue
2. Move the issue to a different project
3. Email a response to the original Service Desk email; the reply shows in the closed issue in the old project

Example Project

https://gitlab.com/dotcom-support-testing/sd-project-a/issues/1

What is the current bug behavior?

A note is added to the closed issue (and the issue isn't reopened)

What is the expected correct behavior?

A note is added to the new (moved) issue

Output of checks

This bug happens on GitLab.com