Police said the theft of a mobile phone from a funeral directors in Portslade has been linked with two other incidents that have involved a theft and an indecent exposure.
On each occasion, one or two men have entered premises waving pieces of paper with writing on and apparently having a poor command of spoken English, Sussex Police said.
Police said: "Between 3.30pm and 4.30pm on Monday, February 4, one man went into Jefferies Funeral Services in Carlton Terrace waving a piece of paper and saying something about 'construction work, painting'. One of the men was captured on camera and police would like to speak to him in connection with the incident.
"After he had left, it was discovered that an iPhone X had been stolen.
"The incident is being linked to a man who indecently exposed himself to a woman in a tanning salon in Portland Road, Hove, at 4.45pm and the theft of another iPhone X from a nail bar in Blatchington Road, Hove, at 6.30pm on the same day."
Anyone who recognises the man or as any other information is asked to report online or call 101 quoting serial 189 of 05/02.