How can I catch forwarded calendar invites with an Exchange mail flow rule?

A forwarded invite may arrive as an ordinary email rather than as a calendaring message. So the fact that the original invite contains calendar content does not guarantee the rule will see the forwarded copy as that message type.

Check a failed example in message trace and inspect the actual message properties Exchange evaluates. Then build the rule around a reliable property of that forwarded message, if there is one, rather than assuming the original Content-Type value will be available in the way the rule expects.

I'd start by confirming what the forwarded message actually looks like at the point where the rule runs. The header from the delivered message may not be enough to establish that the same header is present or exposed to the transport rule condition on the forwarded copy.

If you can identify a stable marker, such as a particular attachment or header, test a narrowly scoped rule against it. Be careful with broad matching, since regular emails can also include calendar-related content.

There may not be a clean rule-only fix if Exchange classifies these forwarded items as regular messages. Message type conditions are useful for direct meeting requests, but forwarding can change how the message is represented.

Use message trace to verify the path and compare a direct invite with a forwarded one. If there is no consistent property to match, you may need to change the forwarding workflow rather than rely on the Calendaring condition.