Cross Currency Swap - CFAI Questions

Derivatives P288 in CFAI curriculum books.

Question 3 - B - Part ii - Value a pay £floating and receive $fixed.

Solution on p 298

I can get the £ floating PV of £1.016 and I understand that they are trying to convert this into pound equivalent per 1 USD, but I don’t fully get why they first divide the £ figure by the original FX rate of 1.41 and then multiply it by the new FX rate of 1.35 to arrive at the dollar amount.

I assume it’s related to the fact we have to use the FX rate the notional was calculated at, but would appreciate confirmation.