Here's the moment they informed ATC after it first happened:
"Southwest 1380 has an engine fire, descending"
"Southwest 1380, are you descending right now?"
"Yes sir, we're single-engine, we're descending"
https://vocaroo.com/i/s1z2OzkfUIzs
The female pilot sounds shaken, much calmer on approach on the other snippet I posted. This recording begins at 15:04:45Z on ZNY sector 10 on the liveatc.net audio archive.