He/she is used when the word is the subject of the sentence, the person doing the action. Him/her is used when it is the object of the sentence, the person receiving the action.
Typically in English, the ordering of words in a sentence is subject - verb - object. Like, "Alice punched Bob", "Alice" is the subject, doing the punching, and "Bob" is the object, receiving the punching.
But when the verb is a form of "to be", or otherwise indicates a state of being or becoming, both "sides" of the verb use the subject case. So if someone asks, "Who is there?", the correct response is, "It is I", not "It is me."
In your examples, "Roy and she" follows "is", so should be in the subject case, and "she" is correct. "Roy and her" is the object of "let", and so should be in the object case, and "her" is correct.
Many native English speakers find this does not follow their intuition. They're used to subject - verb - object, so subject - verb - subject just sounds wrong. Thus it's common for native speakers to say "It's me". Or in your example, they would say "It was Roy and her ..." This is technically wrong but so common that outside of an English class you'd probably get away with it.