Backslash to Forward Delete: 1. Fn+Backslash to Backslash 2. retain Shift+Backslash

karabiner_backslash_to_forward_delete.json

{
  "title": "Backslash to Forward Delete",
  "rules": [
    {
      "description": "1. Fn+Backslash to Backslash  2. retain Shift+Backslash",
      "manipulators": [
        {
          "from": {
            "key_code": "backslash",
            "modifiers": {
              "mandatory": [
                "fn"
              ]
            }
          },
          "to": [
            {
              "key_code": "backslash"
            }
          ],
          "type": "basic"
        },
        {
          "from": {
            "key_code": "backslash",
            "modifiers": {
              "mandatory": [
                "left_shift"
              ]
            }
          },
          "to": [
            {
              "key_code": "backslash",
              "modifiers": [
                "left_shift"
              ]
            }
          ],
          "type": "basic"
        },
        {
          "from": {
            "key_code": "backslash"
          },
          "to": [
            {
              "key_code": "delete_forward"
            }
          ],
          "type": "basic"
        }
      ]
    }
  ]
}