G'day Mate
To be fair, you can train a tank crew in just 3 months, but then the quality would be according to the time for training. And some skill/function will not be taught. But yes, it takes more than 9 months for Armies to train their tank crew in general.
When you consider individual training. Driver and Loader are skill based, while gunner and commander is experience based, generally you learn gunnery as a loader, then if you have enough experience, you will be promote to gunner. That is how the system work in the west. Driver, they have to go in with their own training. While commander is basically a graduation of one or more job.
Driver learn how to drive a tank, they need several month to get comfortable in all aspect on commandeering a tank, both turned out or turned in. Driving a tank turned out is like driving a truck, with no windscreen, you sit upright and you cannot see anything behind the shoulder and both bottom corner. But driving a tank turned in require a different set of skill. It would be like you paint the windscreen of your car black, then leave a tiny rectangle in the centre of the windscreen clear, then you drive along the road and tell you not to knock over anything on the side of the road, if you can do that, you can drive a tank turned in. You have to be precision about when you have less than flattery visibility, because you usually use tank with infantry, if you turn and you can't see what next to you, you may ran over your own people.
Then the gunnery, gunnery is not just skill you acquire from training, because there are more to it then firing the main gun. You need to calibrate the sight, look after your equipment and train the gun to where you want to shoot. You can learn all these in tank school, but how to adjust the sight to suit your own and how to allow that tiny drop the firing computer did not account when you are up and down about off-road, that take experience. In Australian Army, we have a regime to train the "Range Compensation" where a gunner look at a target thru computer monitor and manually adjust the gun setting. That system is not cheap, and if you can't do it on a computer, you will need to do it for real.
Finally, about teamwork, a tank have 4 crews, Gunner, Loader, Driver and Commander. The first thing you look at is there are 4 different jobs, but they have to work together as a crew. You can train individual to fill a certain position, like training a gunner about gunnery and training a driver how to drive a tank, but to work as a crew, you need to standardize the training. Otherwise there will be a gap regarding command and quality amongst each crew. So unless you have a school for all the crew who receive the same training on the same standard, each crew cannot be replaced with an "Outsider" so if one of the crew member in a particular tank is down, the whole crew, the other 2, will be useless and out of commission too. And for a perfect crew in combat, one member need to know another member's job, if the commander is down, the loader takes over, if the gunner is down the commander took over. If the driver is down, then the loader or the commander will need to take over. That mean cross training, experience and standard. Sometime not going to get for just 3 months.
Having said all that, there are possibility that anyone can be a tank crew in 3 months, just how much of a quality you are talking about, it is not going to be a standard crew, nor will it be a competent crew. But then, not knowing the quality of Ukrainian Force, so maybe the rebel can fight them with just 3 months worth of training, though as a tanker myself, I do not think that is possible. That's my fair shake of a sauce bottle.
Davo