The high prevalence of depression in society has given rise to the need for new digital tools to assist in its early detection. To this end, existing research has mainly focused on detecting depression in the domain of social media, where there is a sufficient amount of data. However, with the rise of conversational agents like Siri or Alexa, the conversational domain is becoming more critical. Unfortunately, there is a lack of data in the conversational domain. We perform a study focusing on domain adaptation from social media to the conversational domain. Our approach mainly exploits the linguistic information preserved in the vector representation of text. We describe transfer learning techniques to classify users who suffer from early signs of depression with high recall. We achieve state-of-the-art results on a commonly used conversational dataset, and we highlight how the method can easily be used in conversational agents. We publicly release all source code.