API Call/Request for Single Sign On Membership Wordpress Site - repost

We currently have a Wordpress membership website that is in development. We use the Optimizepress 2.0 theme and Membermouse Plugin. We are also using an outside website to provide content to our members. In order for our members to see the outside content they will need to be logged into to the second website at the same time that they login to our website. The partner website provides an API for Single Sign On. We need an API POST request written using the specific parameters provided by our partner website. This API Request will be installed on our website, and in functionality will log our members into both services at the same time. This project should be very easy and take no longer than 15 minutes for someone who knows what they are doing.