Dear Ron, Can I use a 243 Winchester tip to recharge the 6mm Remington?

Q: Hello, can I use a 243 Winchester tip to recharge the 6mm Remington?

A: You're on the right track, buddy, but let's get our terms straight. First, that tip you mention is known as a bullet. "Recharging" a 6mm Remington means reloading it, right? So, technically you would "recharge" the case with a proper quantity of powder. Then you would seat the bullet atop that powder by pushing it into the mouth or neck of the brass case. 

Are we on the same page here? If so, let me go over the steps just to make sure, and I apologize if you already know all this and we're just confused over the words. But words matter and using the wrong ones while handloading ammunition could get someone or some firearm hurt. 

To handload or reload your 6mm Remington cases, you must first clean them, then lubricate them, then run them into a resizing die. This die pushes out the old primer, squeezes the case down to its specified shape/size so it'll properly fit the rifle's chamber. After sizing, clean off the lube and press a fresh primer into the primer pocket. Then add the powder as specified in a handloading manual or guide. Then seat the bullet into the neck. Done. 

There are several fine-tuning pieces of this operation I haven't time to go into here, but I'll assume you know and understand those. If not, procure a handloading guidebook to get the details. 

Finally, the simple answer is that bullets atop 243 Winchester cartridges are the same diameter (.243") as those atop all 6mm cartridges, so you could pull the bullet from a 243 Win. and stick it in a 6mm Rem case, but it had better be the proper weight for the powder charge in that case or chamber pressures could get too high. 

Whew. How's that for a long-winded answer?