I was wrong:
Written

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If you take a written, let it expire, and change companies, it is no longer valid. That is what every person who has come here has said, and we have done about 75 since I started. No it doesn't have to be the same carrier, but you must be employed by a 121 carrier without any gaps in your employment. If you quit the company, and don't get hired until sometime later, than your written is no longer valid.

This is a topic in the ' training ' portion of APC