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Are you both currently at your home residence or address listed with your Apple ID? If either if you is traveling and away from that location it might fail. Double check that both iPhones are updated to the same iOS. But beyond that, your husband will need to talk to Apple Support at 1-800-MY-APPLE. He may get transferred to an Apple Card Specialist at Goldman Sachs Bank and they may transfer him back to Apple if they suspect a technical issue. I’m inclined to think there is an issue on the banks end, but can’t rule out technical.

Delete the invitation you currently have. Then have your husband see if the invitation is still showing on his iPhone. If it is, he needs to delete the invitation also.

Have you travelled recently? Are your regions set correctly? Are you and your husband both physically in the US right now?

Change the language and region on iPhone - Apple Support

Change your Apple ID country or region

Is your iOS up updated in your iPhone?

Update iOS on iPhone - Apple Support

Have you removed/deleted the VPN and its software? Even if it’s turned off, some VPN software and profiles have been know to interfere, even when the service is turned off.

If you’ve used a VPN, Network Settings need to be reset.

Reset your network settings

If you're using iOS or iPadOS 15 or later, tap Settings > General > Transfer or Reset [Device] > Reset > Reset Network Settings.

If you're using iOS or iPadOS 14 or earlier, tap Settings > General > Reset > Reset Network Settings.

This also resets Wi-Fi networks and passwords, cellular settings, and VPN and APN settings that you've used before.

If you adjust any settings or perform any resets, please do a forced restart of your iPhone before attempting to add the card. A forced restart is more than just turning the iPhone off and on. Please follow the instructions in the Apple Support article I linked below.

Force restart iPhone - Apple Support

Is your husband sending an invitation to become a Participant (Authorized User) or a

Co-owner?

Is the invitation removed from both your iPhone and your husbands iPhone?

So, accept the invitation.