a valid residence and work permit is only one of the requirements for non-EU citizens for being eligible for dagpenge.
Since January 1, 2019 a new residence requirement came into force, saying that a person can only get dagpenge, if he/she have been living in Denmark at least 5 out of the last 12 years (the requirement is 5/12 in 2019, however this will be 6/12 in 2020 and 7/12 from 2021). Read more about the residence requirement.
Beyond these 2 requirements (work permit and residence in DK) which is of most relevance for non-EU citizens, then a non-EU person also have to meet the rest of the requirements for being eligible for dagpenge:
1. A person must have been member of an A-kasse for at least 1 year.
2. have had income (from work) during the last 3 years of at least DKK 233,376 kr. (in 2019) in total. And only income from periods where you have been member of an A-kasse can be included.
Transfering of work and insurance periods from other countries is only possible for EU citizens moving between EU/EEA countries, or for non EU citizens moving between the nordic countries.
So, if the person have been member of an A-kasse and have worked in another nordic country there would be a chance to transfer the earned rights to a danish A-kasse, and use it to qualify for benefits from a danish A-kasse. But you dont write if this is the case.
A special way to qualify for dagpenge, is as you write your self, by having completed an education of at least 18 months duration. However this is only possible if the person lived in Denmark the day before starting the education and again at latest 14 days after finishing the education. Graduates do not need to meet the above two mentioned requirements (membership period and income-requirement).
So, there is no possibility to receive benefits according to the information you have given us.