1520s, from French imitateur (14c.) or directly from Latin imitator "a copyist; a mimic," from imitari "to copy, imitate" (from PIE root *aim- "to copy").
1550s, from French imitable (16c.), from Latin imitabilis "that may be imitated," from imitari "to copy, portray" (from PIE root *aim- "to copy"). Related: Imitability.
1824, "a work of art made in exact likeness of another and by the same artist," from Italian replica "copy, repetition, reply," from replicare "to duplicate," from Latin replicare "to repeat," in classical Latin "fold back, fold over, bend back," from re- "back, again" (see re-) + plicare "to fold" (from PIE root *plek- "to plait").
Properly, a duplicate work made by the same artist and thus considered as an original, not a copy. General sense of "any copy, reproduction, or facsimile" is by 1865.