How to do this effect in photoshop

As others have mentioned, you need to use a displacement map to achieve this. But it looks like whoever mad this started with an image of the couple. For the next step I would use a gradient map adjustment layer to give the brown tones and luminosity range of the rest of the image. It looks like the darkest brown color clips the shadows and highlights to give a high contrast image, but then the actual browns selected for the map gives the flat appearance. I would then create a duplicate of the image and change the browns of the gradient adjustment layer to black, and adjust to get a strong black and white. Save that as a psd for your displacement map. Next, back to the main file, I create a alpha channel to isolate the person on the right. I would apply this alpha channel/mask to the gradient adjustment layer, so that the person on the right is a normal image. Next you need a file with the writing. Add that to the main image. Extend it outside of the canvas. If you placed that image as a smart object, raster it then crop the image to make sure there is no longer any parts of the hand writing layer outside of the canvas. Then convert the hand writing layer back to a smart object. The reason you need to do this is that the displacement map and the layer to be displaced must be the same size. Next apply the displacement map to the hand writing layer. Use the alpha channel to apply a mask to the hand writing layer. 

We've had some excellent threads on Photoshop displacement maps here over the years.  This one is one of the best

https://community.adobe.com/t5/photoshop-ecosystem-discussions/wavy-text-maybe-displacement-map/m-p/9008622

Have a play and get back to us if you get stuck or the results are not what you expect.  Something I'll point out from your example is that the closely spaced, and apparently handwriten text, lends itself well to distorting with a displacement map.

Hi,

Type in "displacement map photoshop" in google, it should get you some tutorials for this effect. Althought to achieve this result you might need more manual work.

Regards,