Can I still get a free 144hr visa in Beijing if I have transited another Chinese airport first?

I want to go to Beijing for my 144 hour stop over on my way from NZ to UK. The flights I'm being offered go to other Chinese cities then I must fly on to Beijing. Route is: Auckland - Shanghai- Beijing and to fly on I am offered Beijing - Baku Heydar Int - London. Can I still get a free 144hr free transit in Beijing if I have transited another Chinese airport first?