The process of going to the New World doesn't need much elaboration. In short, when everyone opened their eyes, they were already standing on a hillside.
By the way, Duanmu Huai's form was still his avatar and not his true body— it seems he can only maintain this appearance until he resolves the issue with the Magic Girl.
Besides Duanmu Huai, Ann naturally accompanied him, along with Tomoe Mami and Tamaki Iroha and... Mugeng.
That's right, Mugeng came along too.
Initially, Duanmu Huai didn't plan to bring her, but as soon as Mugeng heard that Ann could come, she insisted on joining, so Duanmu Huai thought it would be helpful to have an extra person to help with fights and carrying luggage, and he brought her along. The others stayed back in Kaname City to continue dispelling rumors... after all, the work needed to be done.
"Is this another world?"