From the question, my understanding of the background is that the husband earned some income in the US at a time when he was a UK resident. He gifted the cash representing this income to his wife, and claimed the remittance basis for the relevant year.
His wife used the cash (perhaps along with other funds) to buy some US mutual funds. Therefore, as regards her husband, each of the purchased funds is considered a mixed fund. The mixed fund rules apply to “property”. Each of the funds is a separate property.
When some of the funds are sold and the proceeds remitted to the UK, the amounts of the gifted income attributed to each of the funds sold is deemed to be a remittance by the husband, despite the funds then belonging to his wife.
Separately the wife is taxable on the gains made on selling the investments. As the mutual funds are not UK reporting, the gains will be taxed as income under the Offshore Income Gains rules.