In this paper we study the focusing of shifted vortex beams of arbitrary order with different polarization. It is shown theoretically that the optical vortex of an arbitrary integer order m, displaced inside a certain axially symmetric beam, is equivalent to the finite sum of the on-axis vortices of orders from 0 to m inclusive. If the order of the shifted vortex beam is non-integer, the sum will be infinite. The fact that the misaligned higher-order vortex beams contain a set of lower-order vortex beams should be taken into account at a signal detecting. It is very actual for communication systems based on orbital angular moments (OAM) carrying laser beams division multiplexing, especially at the distortions and/or wandering of the vortex beams in a turbulent or random medium.Pictures of focused shifted vortex beams, regardless of the order of the vortex and displacement, look approximately the same, as a crescent. To obtain another type of focal pictures, an optical vortex of the opposite sign can be used as an illuminating beam. For the numerical study of the considered effects simultaneously at several optical vortices of different orders, directions of rotation and polarization, a multi-order diffraction optical element was used in the conditions of sharp focusing. It is shown, that named characteristics significantly change the form of rotating intensity in the focal area. It may be useful for optical manipulations.