The other person is PARTLY-WRONG, but that should be expected seeing that the problem's setup and calculations
are difficult enough to easily make mistakes and end up with one or more INCORRECT answers. 

Let number of stamps in Books A, B, and C, be a, b, and c, respectively
After moving  from Book B to Book C, Book B then had  left, and Book C had:   
After moving  of remainder from Book B to Book A, Book B then had  left.
Book A then had:   

After moving  from Book A to Book C, Book A then had  left
Book C then had: 
As there were 240 fewer stamps in Book B than in Book A, in the end, we get: 
                                                                               2a = 3(240) ------- Cross-multiplying
                                                       
                                                Original  number in Book A, or 

As there were 460 more stamps in Book C than in Book B, in the end, we get: 
  
                                                                               ---- Substituting 600 for 
                                                                              14b = 140(45) ---- Cross-multiplying

                                                Original  number in Book B, or 

               Difference between original number in Book A and Book B: 

So, I will accurately divide the entire process by steps.


    (1)  First, he moved 2/9 of the stamps from Book B to Book C. 

    (2)  Then, he moved 3/5 of the remaining stamps from Book B to Book A. 

    (3)  Next, he moved 1/3 of his stamps from Book A to Book C. 

    (4)  In the end, there were 240 fewer stamps in Book B than in Book A, 

                     and  Book C had 460 more stamps than Book B and there were 600 stamps left in Book C. 


First of all, based on description of final state  (4),  we can easily find the number of stamps in each book A, B and C:

          = 600;    = 600 - 460 = 140;    = 140 + 240 = 380.


Next,  I will introduce  arrays of numbers  , ,     ( distribution of stamps immediately before step 1; 
                                                                same as the initial distribution of stamps )

                                            , ,     ( distribution of stamps immediately before step 2) 

                                            , ,     ( distribution of stamps immediately before step 3)

                                            , ,     ( distribution of stamps immediately before step 4)


We just found out the values , , : they are   = 380;   = 140;   = 600.



We will now move from step (4) to step (3).  Marvin's action from step (3) to step (4) was  "he moved 1/3 of the stamps from Book A to Book C". 
                                             So, we can write

     = ,   = ,   =  + .


First of these equations gives  =  =  = 570;  second gives   = 140;  third gives   = 600 -  = 410.


Thus we can fill the row  3 :    = 570;   = 140;   = 410.




We will now move from step (3) to step (2).  Marvin's action from step (2) to step (3) was  "he moved 3/5 of the stamps from Book B to Book A."
                                             So, we can write

     = ,   = ,   = .


First of these equations gives 570 = ;  second gives  140 = ;  third gives   = 410.

It implies   =  = 350;  570 =  =  + 210;  hence,   = 570-210 = 360.


Thus we can fill the row  2 :   = 360;   = 350;   = 410.




We will now move from step (2) to step (1).  Marvin's action from step (1) to step (2) was  "he moved 2/9 of the stamps from Book B to Book C."
                                             So, we can write

     = ,   = ,   = .


First of these equations gives  = 360;  second gives   =  = 450;  third gives   =  = 310.


Thus we can fill the row  1 :   = 360;   = 450;   = 310.


So the answer to the problem question is   -  = 450-360 = 90  stamps.      ANSWER