Nylon Appliqued

Please help me to fix / customise my coat?

I have a very special coat made from Zara the material is nylon and it is burnt on the back. I bought online an applique to cover it but when it arrived I found out it can’t be used on nylon. Do you have any ideas how can I cover the burnt area or if there is anything such as applique, iron on or sew on patches or anything else that I can use?
the coat was a present from my best friend, used to be hers, and I love it! Thanks
Thanks but the problem here is not the lack of creativity, I need to know what kind of material I can iron or sew on my NYLON coat.

put a crown on the back and rhinestone it

Lacoste Nylon Puffer Down Jacket w/ Removable Sleeves 7722334

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