後は任せた！

behind; rear; after; later; after one's death; remainder; the rest; descendant; successor; heir; past; previous; more (e.g. five more minutes); left

topic marker particle; indicates contrast with another option (stated or unstated); adds emphasis

to entrust (e.g. a task) to another; to leave to; to passively leave to someone else's facilities; to leave to take its natural course; to continue (something) in a natural fashion (without particular aim); to rely fully on one's (full strength, great ability, long time taken) to get something done