You current timeline is fine. You’ll notice that the master timecode has shifted a bit but should not be a problem unless you need to hit specific times for specific segments.
If they have the same version of FCP all you need to do is copy your project and media and give it to them. If they’re on a different system then it complicates things. Talk to the editors. See if they’ve done what you want to do, before. Ask them what they expect from you. More information will help be more prepared and save money. This forum is full of very knowledgeable people.
good luck.
joe