You should only be manually updating your ESX if you have a modified version already, in which case it's assumed you have a brain.

This guide will only link to the lines you will need to modify, assuming you are using ESX Legacy from the official repository.

Furthermore, I am only linking the bare minimum for inventory support.

• client/functions.lua
  • L294-L302
  • L746-L993
• client/main.lua
  • L83-L85
  • L98-L129
  • L149-L220
  • L253-L291
  • L302-L309
  • L371-L401
  • L443-L488
• imports.lua
  • Replace
• server/classes/player.lua
  • Replace
• server/commands.lua
  • L35-L126 (ignore 101-108)
• server/common.lua
  • L168-R229
  • L310-L329
• server/main.lua
  • Replace
  • Replace
  • L224-L245
  • Replace
  • Replace
  • L351-L548

Add to server/common.lua

AddEventHandler('linden_inventory:loaded', function(data)
	ESX.Items = data
end)

If this confused you, just download the fork.