Easier for English speakers: donate to Berliner Stadtmission #richardarmitage
Here is a link that will be easier for English speakers to navigate to donate to projects sponsored by Berliner Stadtmission. There are eight projects. Two of them are specifically focused on refugees.
Sharehouse Refugio is a community center for refugees in Neukölln (not the one that Richard Armitage visited, though). They are asking for donations for German instruction (two months).
Flüchtlingshilfe der Berliner Stadtmission is a general donation possibility — mostly for temporary emergency shelters, it seems. Right now they are asking for donations for a clothes dryer, cushions to sit on, and gear for babies.