This letter proposes a deep learning model to deal with the spatial transfer challenge for the mapping of irrigated areas through the analysis of Sentinel-1 data. First, a convolutional neural network (CNN) model called "Teacher Model" is trained on a source geographical area characterized by a huge volume of samples. Then, this model is transferred from the source area to a target area characterized by a limited number of samples. The transfer learning framework is based on a distill and refine strategy in which the teacher model is firstly distilled into a student model and, successively, refined by data samples coming from the target geographical area. The proposed strategy is compared to different approaches including a random forest (RF) classifier trained on the target dataset, a CNN trained on the source dataset and directly applied on the target area as well as several CNN classifiers trained on the target dataset. The evaluation of the performed transfer strategy shows that the "distill and refine" framework obtains the best performance compared to other competing approaches. The obtained findings represent a first step towards the understanding of the spatial transferability of deep learning models in the Earth Observation domain.