Xero inventory sync

We have 3 website stores, 2 physical stores, and 1 warehouse. For sales the 3 websites use Woocommerce, 2 physical stores use Xero, and we need inventory to be in sync. 2 websites send invoices to 1 Xero organisation, 1 website sends to the other Xero organisation, each physical store uses it's own Xero organisation. Each point of sale that changes the inventory needs to sync that change to every other. The solution can be a Woocommerce plugin that connects to the Xero API.