This paper presents Lingua Custodia’s submission to the WMT22 shared task on Word Level Auto-completion (WLAC). We consider two directions, namely German-English and English-German.The WLAC task in Neural Machine Translation (NMT) consists in predicting a target word given few human typed characters, the source sentence to translate, as well as some translation context. Inspired by recent work in terminology control, we propose to treat the human typed sequence as a constraint to predict the right word starting by the latter. To do so, the source side of the training data is augmented with both the constraints and the translation context. In addition, following new advances in WLAC, we use a joint optimization strategy taking into account several types of translation context. The automatic as well as human accuracy obtained with the submitted systems show the effectiveness of the proposed method.