I converted from an OA visa to an OX visa partway through my OA visa.
The process I took was cancelling the existing insurance and starting a new full insurance from the intended start date of the OX visa.
I went with the same insurance company because they had my details and it was a no hassle's process.
Going through immigration, the visa stamp was to the end of our passport expiry date which was 3
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years even though our insurance was only for 12 months. I haven't reached the end of the first 12 months of the OX visa, so I'm not sure of what process they will follow in confirming continuation of health insurance.