Post recovery and migration

A while back, my hosting provider shut me down unexpectedly and I lost a 5 year old WordPress database. My world was slightly sadder that day for I failed to make a proper backup. Lesson learned for the future. I just went to try and make a mobile post from my phone and realized that my phone cached every post from that database. So, what I am looking to do is to figure out if there is a way to migrate all those cached posts from my old site and post them to the new site on the new host? This was all discovered via the latest version of the iOS WordPress app. Any and all help would be greatly appreciated.

P.S. I’ve considered manually copying and reposting each post, but somewhere in the neighborhood of 300 posts is far more of a tedious job then it needs to be. I’d be grateful for a much easier way.

Kindest regards,
Christopher