Copy/Paste from TextEdit WhatsApp convo: emojis go to pink X's

I have a txt document of a long whatsapp conversation. The emojis show up perfectly in the txt doc. If I copy/paste or if I import the conversation into InDesign, the emojis become pink highlighted Xs.

If I highlight one and change the font to Apple Emoji, the correct emoji appears.

Problem is the conversation is long enough that there must be a more automatic way to do this for the whole document than highlight and change each one. Any suggestions?

Thanks