Fill uneven space between shower tile and door frame

I had a family friend re-tile in my shower, put up Durock and installed a new tub. Everything looks OK, except this gap between where the Durock and tile meets the bathroom door frame. He was unsure how to finish it. And is on the outs as a family friend as a result. Please help me repair this, I need suggestions for DIY, to repair the friendship as well....

 

Another view of the area needed to be filled

 

Since the edge of the tile is not finished and uneven I would try to cover it as well as the gap. I'd make up a wood filler/trim strip to bridge and conceal the gap and cover maybe 1/4-1/2" of the tile. Paint it white and caulk the edges.

 

Reason #729 that you don't hire friends to do renovations. You are going to have to probably custom make some sort of molding. Take a measurement of the depth of the backer and tile and look to see if you can find any transition molding from a flooring dept or store. Specifically ask for floating floor molding.

More importantly, I note that white mortar was used. Did your friend use thinset mortar from a bag that had to be mixed or did he use a ready mixed stuff from a tub? If he used the tub (mastic) it is not rated for a wet location and therefore can not be used in a shower application.