i have completed the future intuitive project more than once but every time i complete IH i get the project again. i do have video. i can craft the pieces for the project.
https://youtu.be/MyhEnBe1APA
The same thing happened to me. I finished Iron Horse and finished the Future Initiative project last week. This week I beat IH again and it re-gave me the Future Initiative Project. I have the crafting blueprints for the whole Future Initiative already. I did not finish the Foundry Bulwark set yet, but that aforementioned run gave me the piece I needed to do so. I am going to finish both projects FI for the second time and FB for the first time before raiding again.
I will re-finish FI and then finish Foundry Bulwark project and hopefully it will overcome this issue before moving on to gaining the parts of Regulus from another run of the raid. Also to confirm I received the same quest which will give me the same rewards for Future Initiative. I play on Ubisoft Connect/PC same name as here: Post_OfficeCore.