What is the first thing we need to do when the pulmonologist has suggested hospice for our mother-in-law?

I'd suggest checking out the hospice providers in your area. I am assuming you are speaking of in-home care. When I did some research on this topic, I found that different providers offered different levels of services. They were all happy to explain their services over the phone. Choose the one that has the most needed services for your MIL. The MD signs a script approving hospice care. When you select the provider, they come to the home and do an assessment and lot's of paper work. Your MIL will be asked to sign a paper acknowledging that she is not seeking further medical care for her condition. All care going forward will be palliative (making her comfortable). (You need to prepare your MIL for this paper, it's a gulp) If she is on Medicare, get any needed equipment before putting her into hospice. My 2 experiences with hospice (different providers) was very postive and they do wonderful work. Most hospice organizations state that people wait too long to bring hospice in. In my first experience, hospice was involved for less than 3 months. The 2nd experience less than 5 days. My neighbor, less than 1 day. I wish you well at this difficult time.