Diseases of cereals caused by pathogenic fungi can significantly reduce crop yields. Many cultures are exposed to them. The disease is difficult to control on a large scale, thus one of the relevant approaches is the crop field monitoring, which helps to identify the disease at an early stage and take measures to prevent its spread. One of the effective control methods is disease identification based on the analysis of digital images with the possibility of obtaining them in field conditions using mobile devices. In this work, we propose a method for the recognition of five fungal diseases of wheat shoots (leaf rust, stem rust, yellow rust, powdery mildew, and septoria), both separately and in combination, with the possibility of identifying the stage of plant development. A set of 2414 images of wheat fungi diseases (WFD2020) was generated, for which expert labeling was performed by the type of disease. WFD2020 data are available freely at http://wfd.sysbio.ru/. In the process of creating this set, a method was applied to reduce the degeneracy of the training data based on the image hashing algorithm. The disease recognition algorithm is based on the convolutional neural network with the EfficientNet architecture. The best accuracy (0.942) was shown by a network with a training strategy based on augmentation and transfer of image styles. The recognition method was implemented by the authors as a bot on the Telegram platform, which allows assessing plants by lesions in the field conditions.