The very first sentence of the letter seems to suggest she asked her dad to send it so if it's real he prob didnt just do it on his own. But from the fold it doesnt seem like it'd fit into any standard size envelope. (Unless the scale or image is messing me up.) That signature seems super femmy too.
Does she use double spacing after periods in her normal posts? Cause the letter has them.
I could see him sending her an email and then her printing it out and forging his signature. If she's friends with her dad on social media that'd be pretty ballsy to straight make it up.