While I'm not familiar with Singapore policies specifically, with most airline programs and credit cards, the credit card accrue and belong to the primary card holder. If the airline prohibits sharing or pooling, the fact that you are an authorized card holder won't be enough to allow the transfer from his Amex account to your KrisFlyer account.
The ineligible equivalent bank points will be returned to the original
credit cardholder and to facilitate the return of the miles back to the
bank, we would request for the MR numbers of all the persons who had
transferred their miles to your KrisFlyer account.
This part suggests they will just undo the transaction and the points will be returned to your husband's Amex account. If so, that may be the best possible outcome, with nothing lost. But - a big but - I'm not sure I trust them completely, and I'm not sure the transfer is reversible. (Aside, what are you using the miles for? Could your husband open his own Krisflyer account, transfer the miles there, and use them to issue a ticket for you?)
You may need more expert advice than the Info Desk forum; I'd suggest asking a moderator to move this to the Krisflyer (or Amex?) forum, where folks may have more experience.