Reaching a point B in Cartesian coordinate via Euler angles knows its initial point A Euler angles and Cartesian coordinates I have a point A:-
Known it's Cartesian coordinates (X,Y,Z) and its Euler angle Aka body rotation (R,P,Y) respectively  Roll (rotation around X axis) , Pitch (rotaion around Y axis) and Yaw (rotation around Z axis). 
Now I have a point B:-
Knows its Cartesian coordinates only (X',Y',Z') . 
What I need to find is : the "Euler angles / Rotation" (R',P',Y')  if the body changed its rotation to , it will reach point B 
.
I also have the ability to calculate quaternions if needed to 

 A: My interpretation of the problem statement is as follows (please correct me if I've misunderstood):


*

*Given: an initial point $A = (x, y, z)$, an initial orientation $(R, P, Y)$, and a destination point $B = (x', y', z')$

*Find: an orientation $(R', P', Y')$ such that an object at point $A$ with that orientation would be facing directly towards $B$


First, note that the vector from $A$ to $B$ can be expressed as
$$\vec{AB} = B-A = (x'-x, \ y'-y, \ z'-z)$$
There are actually infinitely many different orientations that "point along" this vector $\vec{AB}$.  To see why, imagine an aircraft doing an aileron roll while flying from point $A$ to point $B$.  The aircraft's direction of motion is always pointed towards the destination point $B$, but its orientation is constantly changing throughout the maneuver.
So, we only need to find one possible orientation meeting the above criteria.
We can think of an orientation as a 3D rotation applied to the default coordinate axes.  There are many distinct ways to represent rotations, as outlined in http://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions.  (Conveniently, this article also defines conversions to and from the various formalisms.)
Let's work with the rotation matrix representation.  First, let's say we want the unit vector $\hat{x} = (1,0,0)$ to map onto the unit vector
$$\hat{u} = \frac{\vec{AB}}{|\vec{AB}|},$$
which means that $\hat{u}$ gives us the first column of the rotation matrix.
Since the transformed axes ($\hat{u}$, $\hat{v}$, and $\hat{w}$) must be mutually orthogonal, we know that the second column $\hat{v}$ of the rotation matrix must satisfy $\hat{u}\cdot\hat{v}=0.$  That is, $$v_1 u_1 + v_2 u_2 + v_3 u_3 = 0.$$  And, since $\hat{v}$ must be a unit vector, $$|\hat{v}|^2 = v_1^2+v_2^2+v_3^2 = 1.$$
With two equations governing three unknowns, we have one degree of freedom remaining.  (As with the aileron-roll example, we've fixed the direction in which one transformed axis will point, but the coordinate system is still free to rotate around the transformed axis.)
Let's arbitrarily pick a value of $\hat{v}$ with zero $z$ component and a positive $y$ component; that is, let's set $v_3=0$, solve the (quadratic) system of equations, and pick the solution that yields $v_2 > 0$.  (In rare cases where $\hat{u}$ lies exactly along the $y$ axis, forcing $v_2 = 0$, we can choose a slightly different, but still essentially arbitrary, constraint.)
This gives us two columns of the rotation matrix.  We can solve for the final column, $\hat{w}$, by again using the unit-vector and orthogonality properties.  The quadratic equations should have two solutions, but we'll pick the one unique solution that satisfies the same "right-hand rule" that our initial coordinate system satisfied (typically $\hat{u}\times\hat{v}=\hat{w}$).
Now, with a full rotation matrix, we can translate this into a roll, pitch, and yaw using the conversions listed in the "Rotation formalisms" article cited above.
Note: in order to get a unique answer, we had to introduce an arbitrary constraint along the way, when solving for $\hat{v}$.  Other constraints might be equally valid, depending on the use case.  For instance, one approach would be to specify that the roll $R$ should remain constant ($R = R'$).
