You have to experiment with different settings and ammunition.
Clean it thoroughly. Check the magazine. Try different ammunition. Check the extractor.
As long as both the rifle and the revolver are chambered in .44 magnum you can use the same ammunition for both. I have a Henry rifle in .44 mag and a Ruger redhawk .44 mag and I use the same ammo for both. That's one of the nice things about that caliber.
300 win.
The caliber of ammunition the rifle uses is usually roll-stamped on the right side of the barrel, just in front of the receiver. For example: if it says "7mm Remington (Rem.) magnum (mag.) you would need to buy that type of ammunition as sold by Remington, Federal or any of the other companies offering this type of ammo in whichever bullet weight you prefer to shoot.
Only use ammunition that is labeled on the barrel of the derringer. Never try to use anything else. If it says 22 Mag, then ONLY use 22 Mag.
Generally when someone says 7 mm they are referring to a 7 mm Remington Magnum. There are several other 7 mm chamberings but 7 mag is the most popular in the US.
Check Wal Mart stores that carry ammunition for guns.
300 mag is much bigger bullet
That doesn't make any sense as a question and not only did Remington not make this gun no-one could have made a lever action firearm in 1846 there was no suitable ammunition much less 44 mag.
There is no "one" better anything- including rifle calibers. The .300 Win Mag can fire a heavier bullet a longer distance, but is generally a heavier rifle, has more recoil, and you can carry less ammunition.
You can find a 22 mag cylinder for a 22 mag revolver mod 21S MIW Germany on eBay. You may also be able to find one through antique sales and antique gun collectors.