Saving breast milk after the breast milk has been heated is not recommended but I have reused heated breast milk after I've frozen it or refrigerated it and never had any health issues with the babies drinking it.
Just make sure the breast milk smells okay and has not gone sour and if it smells bad or sour then throw it out but as long as the breast milk that has been heated and frozen or refrigerated smells okay then it's safe for the baby to drink.
Once you pump breast milk the breast milk will last up to 6 hours at room temperature.
However it's best to refrigerate any unused breast milk within 30 minutes to an hour of pumping it to prevent bacteria from growing in the breast milk.
After you warm up breast milk the breast milk will last up to 4 hours before it goes bad so refrigerate the warmed up breast milk that is leftover as soon as possible.
When you warm up breast milk you should either feed the breast milk to your baby right away or place it in the refrigerator.
Never leave the warmed up breast milk out of the refrigerator longer than 30 minutes or so because the breast milk can go bad.
If you feed your baby the warmed up breast milk and there is any leftover you can refrigerate the leftover portion and then reheat it again to feed it to your baby.
It's recommended to not reuse breast milk that is leftover but I always kept the breast milk that was leftover in the refrigerator and fed it to my baby again as long as it was okay.
I never had any issues feeding my babies left over breast milk that has remained refrigerated or frozen.