Kalidasa has written the story of Sakunthala borrowing the idea from Valmiki Ramayana.

Valmiki Ramayana kishkindha Kanda Sarga 44 Sloka 12

dadau tasmai tatah pritah svanamangopasobhitam /
anguliyam abhijaanam rajaputryaah paramtapah //

Rama gave to Hanuman the ring with his name engraved
to be given to Sita as a token of recognition.

Now let us see the Sakuntala Story.

When Dushyanta met Sakuntala and married her in the Gaandhrava style,
he gave her his ring. Then he departed to his Capital. Later Durvasa visited the
asram, but Saknthala was thinking of Dushyantha and did not attend to him.
Durvasa then cursed her that her husband would not remember her. But Anasuya
her Sakhi pleaded with Durvasa not to be so harsh. Then Durvasa said that Sakunthala
can show the ring, the king would remember her.

When Sakunthala was being taken to the palace, she went to river to drink water. At that
time she lost the ring. When she reached the palace and wanted to be accepted as a
wife, he did not remember her. At that time looked for the ring, but he had lost it.
Sakunthala had to go away and live in a forest. Later one fisherman caught a fish which
had swallowed the ring. When he wanted to sell the ring, the king's policemen arrested
him and he was taken to the king. When the king saw the ring, he remembered Sakunthala.

In the Ramayana the word abhijnana and the ring are mentioned.

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In the Abhijnana Sakunthalam, both abhjnaana and the ring come in the picture.