Federated adversary domain adaptation is a unique distributed minimax training task due to the prevalence of label imbalance among clients, with each client only seeing a subset of the classes of labels required to train a global model. To tackle this problem, we propose a distributed minimax optimizer referred to as FedMM, designed specifically for the federated adversary domain adaptation problem. It works well even in the extreme case where each client has different label classes and some clients only have unsupervised tasks. We prove that FedMM ensures convergence to a stationary point with domain-shifted unsupervised data. On a variety of benchmark datasets, extensive experiments show that FedMM consistently achieves either significant communication savings or significant accuracy improvements over federated optimizers based on the gradient descent ascent (GDA) algorithm. When training from scratch, for example, it outperforms other GDA based federated average methods by around 20% in accuracy over the same communication rounds; and it consistently outperforms when training from pre-trained models with an accuracy improvement from 5.4% to 9% for different networks.