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Officers believe the jewellery box may have been stolen during a burglary and discarded in the woods by the offender.
PC Scott Barnden, of the East Hampshire Tasking Unit, said:
"We want to hear from anyone who recognises the jewellery box or anyone with information about it.
"If you think it might be yours please contact us as soon as possible."
Anyone with information is asked to contact PC Barnden at Whitehill police station on 0845 045 4545 or 101.
Alternatively call Crimestoppers, anonymously, on 0800 555 111.
Whitehill
Bordon
Surrey
GU35
The location of the incident marked on this map is approximate