Why did they have to make this?

After Mission Control decided to cancel Apollo XIII's moon landing following an explosion of an oxygen tank in the Service Module, the astronauts moved to the Lunar Module in order to save power that was going to be needed later for re-entry.

The only problem with this plan was that the Lunar Module was designed for only two people for a 36-hour period, not three astronauts for 96 hours. They quickly discovered that carbon dioxide was building up fast, putting their lives in extreme danger. They had to change the circular CO2 scrubbers in the Lunar Module for clean ones, but they only had spare square CO2 scrubbers from the Command Module.

In record time, the Crew Systems Division put together an improvised adapter using all sort of weird and random parts, like a flight manual cover, suit parts, and socks. CAPCOM (Capsule Communicator) transmitted the instructions to the astronauts in order to assemble this "mailbox" rig—as they called it—working against the clock and trying to fight the effects of the poisonous gas which was quickly asphyxiating their brains.

REQUIRED EQUIPMENT and MATERIALS

All required equipment is contained onboard within the Apollo 13 CM and LM.

Cover to the Apollo 13 flight plan (to cover and protect the hose entry)

2 lithium-hydroxide canisters

Roll of gray duct tape

2 LCG bags

2 hoses from the red suits

2 socks

1 bungee cord (to secure the modified filtration device to the wall of the LM)

PROCEEDURE - 19 steps

https://gizmodo.com/this-is-the-actual-hack-that-saved-the-astronauts-of-th-1598385593

More information about NASA Engineering