Privet Moth larvae in the garden

On Saturday 3 August 2024, our Cat Misty was taking an interest in something by the flowerbed directly opposite the kitchen window, I went to investigate and I could see a large green Hawk Moth caterpillar which was flicking from one side to the other. It was a lime green color being 3 inches in length or 7.5cm long and its girth was about 2.5cm long. The sides of the body and pink and white stripes akin to the pink and white stripes in a stick of rock! Near the rear end of the larvae a large 'spike' pale yellow spike near the tip it was black as if dipped in ink. I moved Misty away and checked to see which species it was a Privet Moth caterpillar, a first for the garden and a first for me too! I raed that one of the food plants was lilac, so I moved it onto the leaves of a Lilac bush we had in the garden. Around 30 minutes later, I noticed it crawling quickly over the grass to the back flower bed.