How to manage the catalogs and photo organization

I need to manague the photos of my bos with my or his lightroom account and my own computer, so that he can see what I've organized by using his lightroom in his computer.

Lightroom is single user software. If you are using the catalog, your boss cannot be using the same catalog. The best you can do is to keep the photos on a disk you can both access, and move the catalog file to your boss's computer when you are done with it, so he can see what you have done.

There are two aspects of organisation here. First, the arrangement of storage folders that the image files live inside. Second, the Catalog adds some additional kinds of organisation, including which photos are imported to the Catalog and which are not, and that depends on Lightroom having access to the image files.

In order to assist this other person using LR, both your computers need to be able to "see" these image files in the same way.

There are three ways to do that:

• you can have a copy of all the images inside each computer, preferably in an exactly equivalent folder. So if in one computer they are all inside "C:\files\lightroom\library" (and I recommend setting up a special non-user-dependent location just for LR managed images, distinct from other sorts of files) - the other computer should also have the same, and the same contents
• you can instead have all the image folders etc on an externally connected drive, which can be moved between the two computers. So long as both computers use the same naming for this drive (and on Windows, so long as the drive letter is also made to always get assigned the same) - that achieves the same thing in effect, but more efficiently. 
• otherwise, also efficient, you can store the images in a network location - a file server or a network attached storage device - which both computers can then see identically - for example "\\NetworkStorage\files\library"

The organisation of the folders may or may not be part of your task. But the Catalog needs to import photos at known locations which are not then going to change around further (except, when LR "knows" this is happening).

If required, it is possible when importing photos to LR to have it either Move or Copy the files you choose to import (and only those) into a designated filing scheme within a chosen storage location. That scheme can be either according to their current folders, or else you can get LR to use a date (of capture) based scheme which IMO works well - unless useful organisational information which is currently only apparent from the current folder names, would get unacceptably lost by doing that (IMO it is more robust as a method, when individual images possess that sort of information directly, rather than only deriving it incidentally from their storage location - e.g. through keywording - perhaps something to move towards).

Then once you've made a new Catalog and imported photos, additional sorts of metadata based organisation such as Collections, Smart Collections, ratings, flags, keywords (tags) etc become possible too. Also you can use stacking, custom ordering of the images etc. And entirely new workflow becomes possible, e.g. Virtual Copies. All of this can only be conveyed to another person by giving them a copy of this Catalog file. That just goes into their computer (the location does not need to be the same), or if saved on an external drive, when that is connected to their computer they can open it there.

The images which are imported should (as above) all then automatically find themselves in the new context. But if they do not, provided the relative sub-arrangement of the folders is the same (easiest if all inside one parent folder), it is easy to re-address such that everything in this Catalog does then reconnect to its respective source data.