Should I tell my mother I didn't use her cash gift for the coat she pictured?

My mother put $400 in my birthday card and said, "Now you can finally get yourself a lovely coat. Send me a picture."

I did need a coat. A week later I found one I liked second-hand for $80, and it fits. I put the remaining $320 towards a desk I'd been saving for. I didn't think I was doing anything sneaky until she messaged, "Have you chosen your birthday treat yet?"

She hadn't asked me to buy a particular brand or return any leftover money. I also know she pictured me buying something new and indulgent, because that's what she enjoys giving. An $80 coat may sound to her as though I turned her generous gift into another budgeting exercise.

Would you send a photo and explain the whole choice, mention only the coat, or offer to put the remaining amount towards something she'd recognise as a treat? I'm happy with what I bought. I don't want protecting her pleasure in giving to turn into pretending I spent $400 on it.