Keep "Let's Encrypt Authority X3" for renewed certificate

Very short answer: no, that's not possible.

However, if you renewed after 60 days like Let's Encrypt advices, you should have 29 days left for your previous certificate. You might be able to re-instate that certificate on your server and fix whatever design flaw you've made in the past (i.e. depend on a static intermediate, which should never be done).

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