The Sun is a giant star while Jupiter is a planet. The Sun shines by converting hydrogen into helium by nuclear fusion, whereas, the helium found on the atmosphere of Jupiter are the remnants from the big bang. For Jupiter to be even considered a star, it has to expand roughly 10 times its width.
Removing the helium from Jupiter's atmosphere is impractical because of a lot of factors which includes but not limited to; distance, surface temperature, escape velocity.
