The 25-year-old man has been charged with robbery, converting criminal property, attempting to convert criminal property and fraud by false representation.
The 19-year-old woman has been charged a number of offences, including an act with intent to pervert the course of justice, fraud and converting criminal property.
They are both expected to appear before Londonderry Magistrates' Court on Friday.
"Police would like to take this opportunity to thank local people for their support and assistance during this investigation," a PSNI spokesperson said.
"This has been paramount in allowing police to place suspects before the courts so quickly."