Facebook and a random act of kindness from a Melbourne police sergeant has been credited with helping officers arrest a 17-year-old alleged thief over a $40,000 burglary.

Victoria police were looking for a person who allegedly stole expensive watches, handbags, foreign currency, credit cards and jewellery from a home in Clarinda, a suburb in south-east Melbourne, in early May.

Officers had obtained video surveillance footage of a young woman using one of the allegedly stolen credit cards and put out an internal memo.

The footage jogged the memory of a sergeant at the Caulfield station, a few suburbs over, police said in a statement.

The sergeant said that days earlier while off duty, he had been travelling on a train when a girl asked him if she could borrow his mobile phone to contact a friend on Facebook.

“Being the kind-hearted person that he is and the fact that he had unlimited data he happily obliged,” police said in a statement.

After seeing the memo, he said he realised he had encountered the wanted burglar.

“With the assistance of some more tech-savvy officers than himself, he was able to establish the identity of the woman and a warrant was issued to search her address,” police said.

Police raided a home in the bayside suburb of Chelsea and recovered the majority of the allegedly stolen property.

They have charged the 17-year-old girl with burglary, theft, obtaining property by deception and possessing a drug of dependence. She is expected face a children’s court later this year.