A car seat is not just another piece of gear, it is a safety device with an expiration date and a permanent retirement rule after any crash. Moving it correctly means protecting the parts that actually keep a child safe, not just boxing it up.
Pro tip: Photograph the current LATCH or seat belt routing before you unbuckle it from the base, so reinstalling at the new home matches the manufacturer's recline angle exactly.
Watch out: Never buy, accept, or reuse a car seat with an unknown or confirmed crash history; even if it looks fine, the internal energy-absorbing foam can be compromised.