Maxson's Battlecoat

Maxson's battlecoat is a unique piece of clothing in Fallout 4.

Characteristics
Maxson's battlecoat is worn by Elder Arthur Maxson, leader of the East Coast Brotherhood of Steel, and consists of a black BOS Officer uniform underneath a heavy padded leather coat with the Brotherhood insignia displayed on the right shoulder. Its already formidable protection can be enhanced even further by upgrading it with the ballistic weave armor mod. While the coat can't be worn underneath additional armor pieces, fully upgraded it offers better protection than the Railroad armored coat V and weighs less. On top of that, it grants a bonus to Perception.

Various terminal entries aboard the Prydwen shed some light on the battlecoat's background and development, even mentioning its considerable weight.

Locations
The battlecoat is worn by Elder Maxson. Since Maxson cannot be pickpocketed, using the Pickpocket perk level 4 will not work. The only way to obtain the battlecoat is to kill Maxson and take it from his body.
 * The simplest way is to kill Maxson aboard the Prydwen. Note that this must be done before starting The Nuclear Option, otherwise Maxson is flagged as essential and cannot be killed, making the battlecoat impossible to acquire, but only if you sided with the Brotherhood. He is still killable if you sided with the Minutemen.
 * If the player sides with the Institute for the end of the game, the penultimate mission Airship Down will have the player raid the Boston Airport and use a synth to hack Liberty Prime and use it to destroy the Prydwen. At some point during the battle, a vertibird will drop Maxson, outfitted in a full suit of T-60f power armor. The player must ensure to loot the battlecoat before the Prydwen is destroyed, otherwise Maxson will disappear along with his clothing. The best way to eliminate Maxson in time is to have the synth hacking Liberty Prime destroyed, and staying at the bottom of Liberty Prime's gantry. As long as the player doesn't reach the top of the gantry, the synth will not respawn, thus giving the player plenty of time to kill Maxson, loot him then continue the mission. This method also allows the player to obtain Maxson's unique power armor with the Elder paint mod, and his unique weapon, Final Judgment.
 * If the player sides with the Railroad, the mission Rockets' Red Glare will have the player sabotage the Prydwen. After planting the bombs, when exiting the Prydwen, Maxson will be in the Command Deck, where he can be killed and his battlecoat and the Final Judgment Gatling laser can be obtained.
 * An easy way to kill Maxson is to upgrade the railroad gun that Desdemona gave you during Precipice of War to its maximum killing ability. When you enter the Command Deck, target his head immediately using VATS.  If you have upgraded your rifleman and Ninja abilities sufficiently, he will be killed with only two or three shots.  You can take care of the other two in the same fashion.  Depending on your armor, you may walk away with both the Final Judgement and Maxsons Battlecoat with some minor injuries.
 * It is possible to obtain the coat during the quest Show No Mercy to push Maxson off the Prydwen's deck; the resulting fall will most likely kill him (unless he lands in water) allowing you to simply loot the coat from his body (WARNING: it is unconfirmed but if you do this method the Brotherhood may turn hostile because of Maxson's death but shouldn't since you never attacked him)