There is a good book by Koivo about robotic manipulators.  I have derived the inverse kinematics equations only for a 5DOF, but solving for the equations for a 6DOF will not be far from how you solved for a 5DOF manipulator.  Let me know if you want it.

If I understand you correctly, you would like to obtain the homogeneous transformation of the end-effector pose that is defined as 6 coordinates (x, y, z, phix, phiy, phiz). Once you have this homogeneous transformation you are able to solve the kinematics.

In this case you need to create the transformation matrix by combining the translation matrix obtained from (x,y,z) with the rotation matrix obtained from (phix, phiy, phiz). The tricky part is that you must know what (phix, phiy, phiz) are encoding (e.g. Euler 2) to create the correct orientation matrix, several robotics systems use Euler 2 (ZYZ). You could find how to code the rotation matrix depending on how the information is encodedin this Wikipedia entry: https://en.wikipedia.org/wiki/Euler_angles