So as a visual example, here is my Shiny Gyarados from Crystal Version (Top Left).
It's DVs (IVs) are: 0 HP / 14 Atk / 10 Def / 10 SpC/ 10 Spe
When traded to Red Version via time machine, and then transferred to Moon using the PokeTransporter, it gets random IVs (3 at max), a random nature, hidden ability, and loses its shininess. The loss of its sparkle is due to an error in the PokeTransporter's shiny formula. In the formula for Gen 1 to 2, if a Pokemon's Spe, Def, and SpC DVs are 10, and it's Atk DV is 2, 3, 6, 7, 10, 11, 14, or 15, it will be shiny. This means that shininess is stored in RBY, despite many people believing it isn't, as there were no shiny pokemon in Gen 1. This formula is also used when transferring from Gen 1 to 7, however, the Atk and Def are switched. So show this, I edited my Gyarados's DVs and reversed the Atk and Def DVs.
They are now: 0 HP / 10 Atk / 14 Def / 10 SpC/ 10 Spe
I then transferred both original and edited Gyarados's to Moon and you can see the results above, original on bottom left, and reversed Atk/Def on bottom right.