car seat airplane toddler

What’s the best way to pack a toddler’s booster seat for an airplane trip?
Initial question may not be clear will try better here; we’re flying across country in a few days with an 5-almost-6 yr old. Child will not need to use the seat on the plane itself but we need to bring it to use in a car at the destination. Can the booster seat just be tagged as luggage itself and checked? Lash/tie it to a checked suitcase? Put it in a box? Just looking for the best or ideal way to deal with bringing this along.
Note this isn’t a fully child seat; it is for a toddler so there’s no big back; its just a booster seat with short armrests.
I would have them sit on it in the plane even if they don’t need to, it is easier than trying to pack it or strap it to a bag.
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