In this work, we focus on estimating articulatory movements from acoustic features, known as acoustic-to-articulatory inversion (AAI), for dysarthric patients with amyotrophic lateral sclerosis (ALS). Unlike healthy subjects, there are two potential challenges involved in AAI on dysarthric speech. Due to speech impairment, the pronunciation of dysarthric patients is unclear and inaccurate, which could impact the AAI performance. In addition, acoustic-articulatory data from dysarthric patients is limited due to the difficulty in the recording. These challenges motivate us to utilize cross-corpus acoustic-articulatory data. In this study, we propose an AAI model by conditioning speaker information using x-vectors at the input, and multi-target articulatory trajectory outputs for each corpus separately. Results reveal that the proposed AAI model shows relative improvements of the Pearson correlation coefficient (CC) by ~13.16% and ~16.45% over a randomly initialized baseline AAI model trained with only dysarthric corpus in seen and unseen conditions, respectively. In the seen conditions, the proposed AAI model outperforms the three baseline AAI models, that utilize the cross-corpus, by ~3.49%, ~6.46%, and ~4.03% in terms of CC.