A note from Little Moonbeam's father is an audio note Sydney's father left for her as he was dying in the Statesman Hotel. If given to her after she tells of her story, she will part with Sydney's 10mm "Ultra" SMG as thanks for the deed.
The note can be found on the third and uppermost floor of the Statesman Hotel, mid level, close to the center of the building, just south of the marker for the Statesman Hotel restaurant elevator.
If making way up to Reilly's Rangers for the first time, the note is found two floors above where the corpse of Theo can be found on the stairwell. The room it is located within is the first door to the left (facing north looking down the corridor immediately after leaving the stairwell to that upper floor). The door is opposite a locked door, which is a storage closet (easy difficulty) with ammo and med supplies. Just beyond the storage closet is a side-by-side fire hose and med station on the wall. Once entering the hotel room, just look for the illuminated bedroom. The note is on a bed, next to a sprawled out skeleton.
My dearest Little Moonbeam. I know you've been waiting to hear what happened to me.
I'm sorry I left you like I did. An important deal came up... one that might have let us get away from that shack we were living in.
I came to the Statesman Hotel to meet the buyer and the deal went bad. We shot each other, and now I think I'm dying.
I won't make it out of this place... the ruins are crawling with super mutants. All I can do is record this and then hide up in one of the rooms.
You're a strong girl and I know you can use everything I taught you to survive alone.
Please forgive me, sweetie. I only wanted to make the best for us. Daddy loves you very much. Goodbye.