An anonymous tip-off led them to a property where Shaw was staying on January 21.
During a search of the address, police say they found "physical evidence linking [Shaw] directly to this offence", according to a summary of facts at Christchurch District Court today.
But only 1700 pieces of stolen jewellery, valued at $176,000, were recovered.
Shaw admitted one charge of burglary.
Judge Tony Couch remanded him in custody to be sentenced on October 18.
Police are seeking an order from the court for $104,000 in reparation to be paid to La Bu for the unrecovered stolen property, and another $2000 to The Tannery for damage caused during the break-in.