The expansion of mobile devices (e.g. tablets, smartphones) and their educational and recreational applications have contributed to the emergence of Mobile Learning Games (MLGs). MLGs show great potential for increasing engagement, creativity and authentic learning. Yet, despite their great potential for education, the use of MLGs by teachers, remains very limited. This is partly due to the fact that MLGs are often designed to match a specific learning context, and thus cannot be directly reused in other situations. In addition, the existing authoring tools are either simple to use but do not offer enough features for designing MLGs that meet the teachers' needs, or much too complex to be used without programming skills. To tackle these problems, we propose JEM Inventor, a MLG authoring tool, based on a nested design approach, progressively revealing functionalities, depending on users' skills and needs. JEM Inventor and its nested design model were evaluated through two experimentations with more than twenty teachers, from a wide range of fields and expertise with the use of MLGs. We also conducted field experimentations with more than 1500 students in order to evaluate the quality of the MLGs created with JEM Inventor as well as their impact on learners.