Answer
Yes — create the same persistent custom field on the corresponding Historical LU as well, matching name, length, and type exactly to the Active-side definition. The framework has built-in support for transferring custom field values across this Active-to-Historical transition once a matching field definition exists on both sides. Depending on your exact release/patch level, an additional fix may be required on older tracks for this transfer to work reliably — if the value still isn't carrying across after adding the matching Historical custom field, check with support for any applicable patch for your specific version.