Joukaheinen, it looks like since you don't have any sinew and don't want to go through the hassle of getting some, then you basically have 2 options left. Fill it with liquid wood or sawdust and glue, and/or cut a strip to fit the tunnel and glue it in as well. Like Radius said, if you want to put a backing on it, that would be easiest (but you may have to order it). It's up to you. But I don't see it as being a problem. It can be done, it's just however you want to do it. Let us know and good luck!
P.S..... These tunnels like I said in my first response, are somewhat common in White Ash. The poor Ashes (which are a wide variety-Green, Black, White, Blue, etc.) are being plagued with an Emerald Ash Borer insect that is brilliantly colored in emerald, hence the name. I don't know if this is a worm that is doing the tunnels, or if it's the Emerald AB, but I am going through the exact same thing right now with some WA that I cut out of my own woods from a seemingly healthy good sized log. personally, I am using anything with a worm tunnel on the back for firewood, because I have a lot of it (don't have to pay for it) and because the bows I am going to make from it are to be sold, without backing and the buyer wants the wood all natural with no defects. I love WA, but this is it's main drawback.
