Verify a Superpermutation
05AB1E, 4 bytes
ÙœåP

Only takes input \$J\$ (I don't need \$n\$ with this approach).
Try it online or verify all test cases.
Explanation:

Ù     # Uniquify the digits of (implicit) input-integer
 œ    # Get all permutations of this uniquified integer
  å   # Check for each if it's a substring of the (implicit) input-integer
   P  # And check if this is truthy for all of them
      # (after which the result is output implicitly)