Here's a copy of some posts I made on this subject from this thread......http://www.graybeardoutdoors.com/phpbb2/viewtopic.php?p=388927&highlight=#388927Hope this helps clear up the muddy water a bit. 
Better pull it completely apart and give it a thorough cleaning. Pull the buttstock by removing the recoil pad, then a 9/16 socket on a long extension or two together to remove the stock bolt in the bottom of the hole. Remove the foreend and the barrel. You should have 5 parts now; pad, buttstock, action, barrel, and foreend. Flush the action real good from every angle and in every opening you can find with brake cleaner, then quickly follow up with some good lubricant, I use Tri-Flow, but any good one that leaves a teflon coating will work. Let it get alll over the receiver and wipe it off good as this will restore the lustre that the brake cleaner will dull. Next clean and polish that barrel! Use Sweets 7:62 or another good amonia based solvent first, then make 50 passes with some Flitz or JB Bore Bright (not Bore Paste). Then flush it out with some Outers bore scrubber or similiar product, dry patch it really good and then Sweet's it again, and then dry patch really good again, and then apply a light coat of Rem oil or good gun oil. Something else I do, that I've been doing since I was a kid, is to apply a coat of Vaseline to all the metal surfaces, worked 30 years ago and still works now.
Sounds like a lot of work I know, but it will be worth it when you go to the range for the first time. Don't forget to bore-sight your scope beforehand too. You have purchased one the most infamously accurate shooters in a Handi Rifle so feel confident. I'd stay away from those 60 grainers to start with though, probably will shoot them after a 100 or so rounds tho. Good shootin' and keep us posted.
One thing that I did forget to mention is that before I reassemble the gun I BLOW the receiver out thoroughly. I have a bobtail truck with glad-hand attachments for a trailer so I purchased one of the air hoses that attaches to it and I blow the receiver out until it is dry, I mean until I'm sure it's dry of the Tri-flow and only the teflon residue is left. This could be done with the canned air like is used on a computer but would take longer and probably a few cans. I know that one of the blower attachments can be bought at Wal-Mart and maybe, if you can find any FREE air anymore, it could be done at a service station.
I only use the Tri-Flow for lubricant in the receiver, yes, but only after I have blown it out good. Technically anything that is moist or lubricated will collect crud. Just redo the flush before every season and you should be alright. I used to use CLP before I discovered the Tri-Flow.
The brake cleaner will cut just about anything and dries DRY. That's why I use it. But it will make you think it has even cut the blue off your gun too. Just hit it with any oil or gun lube right afterwards and it shines right back up.
One other thing that I do is after I have cleaned the barrel I use a cotton ball wrapped around a piece of cleaning rod dipped in rubbing alcohol and swab out the chamber, this cleans any lubricant out and pretty much stops the stuck cases issue. This can be done before you store it or right before you head out to hunt or to the range, but should be done before you shoot it after this "surgery".
The new Ultra Varmint .243 that I just purchased was the cleanest H&R from the factory that I have ever gotten, but I wouldn't have known that had I not gone thru this process.
Takes about an hour or so after you've done it a couple of times, well worth the effort. My .243 put shots #9 and #10 at .676 center to center.
One question though? Why the brake cleaner treatment? Is it to get the grease off the lockup?
Yea and every other moving part. H&R's are notoriously dirty from the factory and if your gun was never cleaned like this, probably still is. I've handled guns in pawn shops that were 2-5 years old and still had the factory "gunk" on them. You can always tell by rubbing your finger across the breech face and if it comes back black and greasy then there ya go. If your gun is older than one year, if it has a serial number in which the second letter is before a "U" or a "V", then I would clean it really good, heck I'd do it anyway.
