Let's assume, parents bought house for $300K and sold it for $450 eventhough the house was valued at $550. If parents sold the house for $550, since they lived in the house for more than 2 years, no taxes would paid.
Currently, child has a short term gain of $100,000 and you want to see if filing a gift tax form, his gain dissipates. His basis will be the same even if mother files a gift tax.