No, they're not working on the other parts as far as we know, and it's not exactly something you can do in a garage
They could get the high explosives easy enough, but you need a strong and precisely made casing to make sure you're launching everything together to make it as angry as possible for a split second. You also need someone who understands the engineering well enough to actually do it, particularly without testing
And all that to get the bomb... A bomb they'd basically have to drive in. They don't have icbms, the missiles they do have are often intercepted, and they don't have a plane that could get past nearly anyone's air defense.
And at the end of the day, they could just lie and say they have it... The fact the intelligence community doesn't think they're working on the rest of the bomb matters just as much as the ability to make one
Does Israel have nukes? Who knows... So many rumors have gone around about them having them that it's just accepted as true
Do Russia and China have working nukes? What about India and Pakistan? Do the US nukes even still work? No one is sure
It also just doesn't really matter... The only people who actually would ever need their nukes to work are the French, because their nuclear doctrine includes a warning shot