Spoken Language Understanding (SLU) models are a core component of voice assistants (VA), such as Alexa, Bixby, and Google Assistant. In this paper, we introduce a pipeline designed to extend SLU systems to new languages, utilizing Large Language Models (LLMs) that we fine-tune for machine translation of slot-annotated SLU training data. Our approach improved on the MultiATIS++ benchmark, a primary multi-language SLU dataset, in the cloud scenario using an mBERT model. Specifically, we saw an improvement in the Overall Accuracy metric: from 53% to 62.18%, compared to the existing state-of-the-art method, Fine and Coarse-grained Multi-Task Learning Framework (FC-MTLF). In the on-device scenario (tiny and not pretrained SLU), our method improved the Overall Accuracy from 5.31% to 22.06% over the baseline Global-Local Contrastive Learning Framework (GL-CLeF) method. Contrary to both FC-MTLF and GL-CLeF, our LLM-based machine translation does not require changes in the production architecture of SLU. Additionally, our pipeline is slot-type independent: it does not require any slot definitions or examples.