Sorry that presets on Lightroom on your new phone have not transferred in Lightroom.
Are you using a free version of Lightroom on your phone? If so, please note that with the free version of Lightroom mobile, the images and data do not sync across devices. You can export all the images from Lightroom mobile on your old device and then transfer them to the new phone using bluetooth or any other file transfer service. You can also do that using your computer.
For your presets, you can either re-download the presets from the original source or apply the presets to a DNG image, then export the file as DNG with the edits of the preset applied to it. You can them import the exported DNG files to Lightroom on the new phone and re-create your presets using them.