There is not a set form of supporting letter, and it would not be good to copy someone else's letter. Each person should write about how they know one of the couple, then how they came to meet the partner, and that the partner gradually took part in activities of the group of family and friends alongside the person they live with. Say things that they know about the new person - what they like, their hobbies, where they have been together - whatever they can think of that shows that they genuinely know this person, and how they have come to know them better over time since they live with their friend/son/granddaughter or whatever the relationship is.
It is quite normal that the CO asks for more proof to cover the time of processing. They do this to make sure the relationship is still in place before they issue the visa.