Amazon Connect: Recording Calls Transferred to External Numbers from A Contact Flow

Yes, this is possible using KVS (Kinesis Video Streaming). In this case you should use stop media streaming after the transfer to phone number block.

"whatever customer listens/hears" during the call will be recorded via KVS and the third party destination voice will be recorded as part of the "To customer" section. So KVS streaming won't end after transferring to external number.

Refer below link which should give you an example of KVS setup. https://github.com/amazon-connect/amazon-connect-realtime-transcription