Refinance LMI

I understand that if a refinance is done to 90% with the same lender and LMI was paid on the original loan, as 85% LVR, that only the gap between the 85% and 90% LMI is paid.

However, if the loan is refinanced with a different lender and the Mortgage Insurer is the same for both lenders. Does the same rule apply or is the refinance with a new lender going to incur the full amount of LMI.
Original loan was 2+ years ago.

Thanks

Mal

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