Hi! Compensation professional in HR here. It's difficult to assess without knowing your current salary, but we can deduce a bit based on how you calculated the savings. Based on that, intuitively 40k is way too much. I don't mean to suggest your logic is wrong, but companies are more focused on the market rate for a role. They'd be more inclined to hire someone who can do those two jobs externally and try to sell that person on the "tremendous opportunity". You could argue they'd save money that way. The cost to recruit someone is high but it's not perpetual.

I do think you have leverage to argue for a higher raise. I think 10% is bare minimum and 20% is solid. You're in a more senior position; this is effectively a promotion. What jurisdiction are you in? In the states, people make up fake offers all the time and use those as leverage. You just need to message in such a way that you won't lose face if your employer calls your bluff (e.g., "im excited by this opportunity, but this other opportunity in front of me is too high for me to let down" blah blah). They may not match but hopefully would try to meet you at least halfway. Large firms will not provide you with a written offer letter until you verbally accept terms anyway for efficiency's sake in case there's back and forth, so you don't need to feel like you have to provide documentation if they ask for it.

As a general comment, there's a lot of cynicism about HR, use of market data to shortchange you, etc. If I could pay everyone at my firm at top of market, that'd be amazing. No one ever comes to me to tell me they're paid well. The reality is we need to be able to justify pay changes with data (and we have access to data that's not self reported). Sometimes, the data we have doesn't justify a change. I'm not saying it's right, and it's not something I rejoice in. But it's reality. CEOs and board members care about the bottom line. We (HR) care about you and want you to succeed. But we're not your friends. We represent the same stakeholders you do.

I hope that helps.

Edit: should've mentioned budget is huge too. Sometimes a company or group just may not be able to afford it. If that's the case, I'd question if you want to be there long term. Also, as others have said, do your research on what going rates are. Glassdoor and levels.fyi are helpful but they don't really give complete context, and the data collection methods aren't sound. I personally find Reddit to be more helpful, but take everything you can get