The device has a hollow suction nipple device (4) and a single-piece hollow base section (6) placed on a beverage container (18), where the device is made of soft-elastic material such as latex or silicone. The suction nipple device comprises a drinking slot (10) in an end region (8). A terminal part (12) of the base section is rolled up outwardly toward the suction nipple device. The base section comprises a lip (14) at an end, which is opposite to an end of the suction nipple device. The suction device nipple comprises a nipple wall with thickness from 0.5 to 2 mm. An independent claim is also included for a method for attaching a drinking suction device on an opening of an open beverage container.
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