We can detach the NFC antenna from the old battery starting from one of its corners, first heating it a little with a hairdryer. Then we can apply it to the new battery.
To facilitate battery unstuck (which notice is attached tenaciously!), I advise you to proceed as follows. First of all, I found it easier to operate from the base of the battery (where the flexible cable connector starts) since there was a little more room to work than at other points. From here, patiently begin to perform these two actions alternately: heat inside with a hairdryer and gradually introduce a thin object (the one I used was plastic, longer than the battery and about 2 cm wide), also making movements side. If you have a contact cleaner or alcohol, you can spray some inside. You will see that little by little, with patience, you will come up above and the battery will come off!
The small black cover of my phone was also attached with a double-sided adhesive. Therefore, be careful not to force and lift gently.
To facilitate the detachment of these double-sided tapes, I recommend heating with a hairdryer along the edges of the back cover, especially at the four corners.