The star gifted to the president is a hyperstar [referring to a hypergiant star], and said to be around for the next 20 billion years. However, a hyperstar burns its fuel so quickly they only last for 10s of millions of years at most.
After Dr. Mallory incorrectly explains that the still frame of the Indian rocket can't be enhanced, Dr. Chan reportedly simply enhances the contrast instead. But the "lower contrast" image is heavily pixelated with large squares seen throughout, whereas the "improved contrast" version has much smaller pixels. Although image could have been digitally enhanced to produced the later image (contrary to Dr. Mallory's claim) merely increasing the contrast as the claimed would not have done so.
At one point Dr. Chan refers to the star "gifted" to the president as a "gas giant". Gas giants are planets, not stars (all stars are made of gas, so the word "gas" is redundant in relation to a star).