What you are describing is a Virtual Service. The standard way to build a Virtual Service is to generate it with the VSE Recorder or RR pairs. The resulting MQ service model uses a Service Image to generate the response and can use the build-in correlation schemes as a service would, copying IDs from the request to the response.
If you are building your own service model by hand, so it doesn't use a service image, then you will have to do the copying yourself. Make sure the 'Quiet' flag is unchecked on your listen step. The incoming message's Message ID will be saved to the testExec property 'lisa.ibmmq.Recv.MQMD.MessageId'.
Go into the respond step, beside 'Header Properties', click 'Open Editor. Click the '+' button, and select 'Basic' -> 'Correlation ID'
Beside 'Correlation ID', click the gear icon and select 'DevTest Property Reference':
Enter the property name: lisa.ibmmq.Recv.MQMD.MessageId