They reckon Pluto and it moon Charon share the same atmosphere.

At one time in Earths long history the moon was as close as 12,000 miles, a lot like Charon is today.

Did the Earth and Moon at one point in time in history also share the same atmosphere?

What little atmosphere the Moon has consists of some unusual gases, including sodium and potassium, which are not found in the atmospheres of Earth, Mars, or Venus. The Moon may also have a tenuous "atmosphere" of electrostatically-levitated dust. ~ Wiki

The giant-impact hypothesis, sometimes called the Big Splash, or the Theia Impact suggests that the Moon formed out of the debris left over from a collision between Earth and an astronomical body the size of Mars, approximately 4.5 billion years ago, in the Hadean eon; about 20 to 100 million years after the solar system coalesced. ~ Again Wiki

Estimates based on computer simulations of such an event suggest that some twenty percent of the original mass of Theia would have ended up as an orbiting ring of debris around the earth, and about half of this matter coalesced into the Moon. ~ guess what, Wiki Again

They proposed that in the aftermath of the giant impact, while the Earth and the proto-lunar disk were molten and vaporized, the two reservoirs were connected by a common silicate vapour atmosphere, and that the Earth–Moon system became homogenized by convective stirring while the system existed in the form of a continuous fluid. Such an "equilibration" between the post-impact Earth and the proto-lunar disk is the only proposed scenario that explains the isotopic similarities of the Apollo rocks with rocks from the Earth's interior. For this scenario to be viable, however, the proto-lunar disk would have to endure for about 100 years. Work is ongoing to determine whether or not this is possible. ~ hmmm, Wiki



Maybe