FIG. 1 is a plan view of a holder for fixing a mirror embodying my new design; FIG. 2 is a rear view thereof; FIG. 3 is a front view thereof; FIG. 4 is a bottom view thereof; FIG. 5 is a right side view thereof; FIG. 6 is a perspective view thereof; and, FIG. 7 is an environmental view thereof. The broken line showing of the mirror in FIG. 7 is for the purpose of illustrating environmental structure and forms no part of the claimed design.