Yes. You'll receive any interest you've earned up to the date your transfer is completed.
For full transfers, any accrued interest up to the date of your transfer request processed will be prepaid in the final amount sent to your new provider.
For partial transfers, interest continues to be earned on the remaining balance in your Moneybox Cash ISA or LISA after the transfer has been completed.
Interest is calculated daily but paid into your account at the start of each month.