The technological upgrade of power utilities to smart metering is a process that can take several years. Meanwhile, smart meters coexist with previous generations of digital and electromechanical power meters. While the smart meters provide high-resolution power measurements, electromechanical meters are typically read by an operator once a month. The coexistence of these two technologies poses the challenge of monitoring non-technical losses (NTL) and fraud where some customers' consumption is sampled every 15 minutes, while others are sampled once a month. In addition, since companies already have years of monthly historical consumption, it is natural to reflect how the past data can be leveraged to predict and improve NTL on smart grids. This work addresses both problems by proposing a multi-resolution deep learning architecture capable of simultaneously training and predicting input consumption curves sampled 1 a month or every 15 minutes. The proposed algorithms are tested on an extensive data set of users with and without fraudulent behaviors collected from the Uruguayan utility company UTE and on a public access data set with synthetic fraud. Results show that the multi-resolution architecture performs better than algorithms trained for a specific type of meters (i.e., for a particular resolution).