One thing to remember is that Font's are often manipulated for sign work so finding something that matches 100% just by typing a line of text is a bit of a long shot. Most signmakers will have to at least alter the kerning to some degree especially if it is a large sign, one exception might be if it was a font that had been optimised for signmaking to start with BUT the signmaker doing the job would still have to have that particular font
Finding the right shaped letters is the most important part really, the rest can be changed quite easily.
Letterheads site is always a good place to ask this sort of question as someone will normally tell you not only which font it is but also how it has been changed.
Just to add, don't know if it was you that took the picture but when taking pictures of signs try to get as square on to them as possible, makes it so much easier to reproduce. If it's the customer then ask them to take a picture square on & explain why. If you have the right software you can straighten it yourself now but still easier to start with a square on photo.