Almog. You are right, all morning or all morning long. We don't say "all the morning".
But not in English. I can't speak to the Hebrew, but all the + morning is not used in English. I could only find one example that didn't sound very weird in English - "all the morning birds" - when you're referring not to the morning but something else. (Not that it's common, but it doesn't sound that weird in comparison. But only if it was for something like poetry...). All the other examples I found were foreign languages being translated into English, not native users of the language.