i know many have taken similar firearms to africa, so a detailed description in lieu of the serial number on the form4457 should do it. but, one can never predict the ultimate foolishness of some bureaucrat. i grew a beard before my africa trip and my passport photo shows no beard. the immigration clerk in namibia looked at me at least 5 times before stamping my passport. no one else even looked at me twice.

I've been to Africa 3 times to hunt..once in RSA, once in NA, once in TZ and none of my barrels were stamped with serial number on my rifles. All had the actions stamp only. You'll need to fill out gun permits in advance in most every African country and depending what countries you visit on you flights there and back you'll need them there too. List your TC as a break open action,keep the barrel and action attached in the gun case and you won't have a problem.
You may wish to have Air2000 or another like company do the temp. import and registration for you for < $150USD they'll meet you at the plane claim your luggage and speed you thru immigrations/customs/police dept. much quicker than if you try to do it on your own...$150 WELL SPENT!!

i would agree with everything stated above....

keep the action mated to a barrel, be sure receivers sn# is matching to 4457...

do not think you will have a problem....
but....
i would recomend touching base with your ph, he has for sure seen this before!
and will be able to advise on local jurasdiction