How rescuing works in GBA FE.
Whether a unit can rescue another unit is determined based on the Aid stat, which is displayed in game. If a unit A has an Aid stat equal to or greater than unit B's Con stat, then unit A can rescue unit B. The Aid stat is calculated based on the unit's class and the unit's Con stat. The following table shows how to derive a unit's Aid stat.
|\(Aid = Con - 1\)
|Male + mounted
|\(Aid = 25 - Con\)
|Female + mounted
|\(Aid = 20 - Con\)
In order to perform a Rescue, the rescuer has to move adjacent to the unit to be rescued. If the rescuer is mounted, they will be able to Canto after rescuing.
A unit that is carrying another unit at the start of the turn can move to any tile and then drop the rescued unit onto any adjacent tile. Mounted units will then be able to Canto if they have any movement remaining. Units cannot be dropped onto incompatible terrain, for example you can't drop Roy onto a water tile. A unit cannot Rescue and Drop in the same turn. A dropped unit will not be able to move during that player phase.
A unit that is currently carrying another one can move adjacent to another unit with enough Aid to also Rescue the carried unit, then use the "Give" command to transfer the rescued unit. Mounted units will then be able to Canto if they have any movement remaining. A unit cannot Rescue and Give in the same turn, nor Give and Take in the same turn.
A unit can move adjacent to another unit that is carrying another unit and use the "Take" command to transfer the rescued unit, assuming the taker has enough Aid to rescue the carried unit. They will also be able to Drop the unit to an adjacent tile on the same turn. Mounted units will then be able to Canto if they have any movement remaining. A unit cannot Take and Give in the same turn.
Because Give and Take are essentially free actions, you can ferry a single unit a long distance by placing other units along the required path and moving and Giving (or Taking and Cantoing using mounted units) until the last unit, who will Drop the rescued unit to finish the chain.