You're on the right track.
It was actually Joseph who said that the moon was inhabited by a race of tall humans who dressed like Quakers.
However, Brigham prophesied that there were people who lived in the sun. More specifically:
Who can tell us of the inhabitants of this little planet that shines of an evening, called the moon?...when you inquire about the inhabitants of that sphere you find that the most learned are as ignorant in regard to them as the ignorant of their fellows. So it is in regard to the inhabitants of the sun. Do you think it is inhabited? I rather think it is. Do you think there is any life there? No question of it; it was not made in vain." - Journal of Discourses, vol. 13, p. 271)
As anyone familiar with the LDS doctrine you can clearly see that the BOM CONDRADICTS their own theology.
Actually, all Mormon scripture blatantly contradicts itself. For example in this SOURCE. The author provides numerous clear-cut examples with links directly to Mormon Scripture. Some of the examples include:
And these contradictions remain despite thousands of documented changes to Mormon Scripture, which was supposedly either divinely translated by Joseph or provided to him by direct revelation from Mormonisms god.
All of this evidence leads to a most distressing question: How is it possible to claim that Mormon scripture is unimpugnable when it in fact impugns itself?
It is ‘duplicity’, and we see it with delph, as he opines, flipping and flopping, first claiming he was told by God that the Bible is true, the next post telling us he could point out the errors int he Bible for us if he chose to. What is that passage from the Bible, about a ‘double-minded man’ being unstable in all things? ... I think it’s in Proverbs ... The odd thing about Mormonism apologists’ ‘unstableness’ as it manifests in spinning daily, they think they’re dancing before the Lord.