As I told you three days ago when you asked the same question: "Unless your custody order requires something special, there is no such form. The new contact information should be provided to the other parent without delay." Only you know how you effectively communicate with the other parent. If there is a chance notice would be denied, then do it in some way that preserves a record, such as by email. There reason there is no "answer to this simple question" is that there isn't one, unless it is included in your existing order. When it is not, parents are expected to behave reasonably.
Best wishes for an outcome you can accept, and please remember to designate a best answer.
This answer is offered as a public service for general information only and may not be relied upon as legal advice.