Creature is about 5" long and only seen the once. There appear to be tunnels under the lawn and small mole like hills.

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This is the caterpillar of the elephant hawkmoth Deilephila elpenor. They feed, naturally, on bedstraws Galium species but like to feed on fuschias in gardens. When threatened, the larvae retract their head which protects this area but also inflates the body and enhances the eye spots just behind the head: