Thank you for reaching out to us and Welcome to the community!
If his or her asylum claim has been denied in Greece, unfortunately the Dublin III Regulations apply in their case. That means: any other country they apply asylum in will check the European database and find out he/she already applied for asylum in Greece - which gives the country grounds to deport them back ("transfer").
Please have a look at these previously answered threads from our platform for more information:
Is it possible to appeal elsewhere after getting a negative reply in Greece?
Does Dublin III effect me if I seek asylum in Italy?
You can, however, appeal the decision. It may be best to reach out to a legal aid service for refugees, for example the Greek Council for Refugees, as they can have a closer look at the case and discuss options. Here are their contact details: https://www.gcr.gr/en/epikoinonia-en
Feel free to reach out to the community again if you need any further assistance.
All the best,