The move functionality doesn't support any field edits - it's purely to allow you to move an issue while keeping it valid for the new configuration it might be landing in. It's a minimal amount of process to do one thing properly.
You'll have to find or write a new move process that can change arbitrary fields outside the context of "keeping it valid". Or, you could find/write a listener that can listen for "issue moved" events, scan the moved issue and change the assignee after the event.
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