It is true that polyester can also be made by recycling plastic.
Polyester and certain types of plastic products are made using the same compound. It is therefore possible to make polyester threads be carefully recycling those specific plastic products.
The compound used for making polyester thread is called Polyethylene Terephthalate which is also known as PET. This compound is widely used in manufacturing of plastic bottles for packaged drinking water and/or soft drinks.
Specifically controlled operations in a series of steps are used to recycle plastic products into polyester threads which can later be used to weave the required polyester fabric.