Yes, in a sense. Mormons believe that we all lived with God before we were born on this earth. We believe that we were all “spirit children” of God (don’t ask me how God “begat” our spirits, I have no idea), and that among that population of spirit children was Satan, then known as Lucifer, and Jesus Christ, God’s firstborn spirit child. We believe that God presented a plan for how we could become like him. It involved all of us being born into this life, experiencing mortality and everything that goes along with it, and then returning to live with God again (and do a bunch of other stuff but it’s not relevant at the moment).
The problem was that we would make mistakes (sins) while here, and if we weren’t pure then we couldn’t return to God and be like him, so there had to be a way to allow us to make these mistakes, and then get cleaned up, so to speak. Enter a Savior, or Jesus Christ. Christ would be born, live a perfect life, and then sacrifice himself to pay for all our sins. Don’t ask me how it works. With some difficulty I can imagine somebody suffering the pain of all our sins, but I don’t get how that gets rid of our sins. That’s one of things I accept as “I guess I’ll understand some day.” However, just because we could be saved didn’t mean everyone would be. Some would choose to reject Christ’s sacrifice, and therefore wouldn’t be able to return to God or become like him.
Lucifer presented a different plan. His plan was that God would give him, Lucifer, God’s power, and Lucifer would come down on earth and make sure that no one could sin, that nobody would make any mistakes, nobody would suffer, and so there would be no need for a Savior and everyone could return to live with God. I’m not sure how he planned on doing this, but it kind of sounds like socialism.
God said no, that’s not the plan. Lucifer rebelled against God, and convinced a third of everyone else who was there to rebel as well, and so Lucifer was kicked out of Heaven along with however many billions of people wanted to follow him. Where was he kicked out to? The earth, where we are. And now he and his friends go around as “the devil” and “demons” (which we don’t believe have horns or pointy tails) trying to make us do bad things so that we’ll end up miserable like they are. How do Lucifer/Satan and his buddies do this? I don’t know. The scriptures say that Satan “whispers in our ears”. Maybe when your wife is out of town and you’re driving by the grocery store and in your mind you think “I could sure go for five or six pints of Ben and Jerry’s right now” and then something says “No, you really shouldn’t do that, it’s a bad idea” and then you think “But when am I going to have this chance again?”…well, maybe that’s Satan somehow putting those thoughts of a hedonistic, ice cream-filled lifestyle in your head.
So yes, we believe that Jesus and Satan/Lucifer were both spirit children of God, as we believe we all are.