all communications for those products, services and accounts offered or accessible through
You 'gotta love the word "all!" The only open question is whether the new account is the same set of accountholders as the one when you obtained consent. Let's say you obtained consent from mom for an account that's in her name only. The new account might be in name of mom and dad, mom and child, etc. You're OK as long as legal/regulatory communications only have to be delivered to one of the joint account holders, and mom can be the designated recipient. Should a regulation-mandated notice or disclosure have to be sent to one or all of the other joint account holders, you'll need to be sure you have consent from the others. Remember that each regulation has its own unique set of delivery requirements, so the need to consider the consent status of the other account holders will depend on which regulations apply the the account at hand.