Not a problem.
In order for him not needing to write letters, your sister would not need sole custody, but sole guardianship. That is something totally different than custody. Custody merely relates to who has control over the physical person of a child, whilst guardianship relates to making legal decisions on behalf of a child.
By default, both parents have guardianship and therefore, both parents need to agree on the legal decisions made on behalf of a child. So, something like applying for a passport or applying for a visa would be an example of that.
If, however, the court makes your sister the sole legal guardian, then that would necessarily mean that the father is no longer a guardian and no longer have the power to make those decisions on behalf of the child and, by extension, letters from him is no longer needed.
Unfortunately, only the High Court can entertain such an application and she would have to proceed to an attorney to assist her in such an application. The fact that the father is not going to oppose it, should mean that it would be less expensive and less time consuming.
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