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Juan, nice rifle. Buds has several excellent 44 Hog/Deer loads available. 1): https://www.budsgunshop.com/catalog/product_info.php/cPath/656_2081_10000571/products_id/36396/Federal%20F44SF1%20Fusion%20Sp%2020RD%20240gr%2044%20Remington%20Magnum/ ---- 2): https://www.budsgunshop.com/catalog/product_info.php/cPath/656_2081_10000571/products_id/718001226/Remington%20HTP%2044%20Rem%20240gr%20SP%2050/bx%20(50%20rounds%20per%20box)/ --- My go to for high performance ammunition is Underwood : https://www.underwoodammo.com/collections/handgun-ammo/cartridge_44-remington-magnum

what you have ( winchester .44mag 240 gr JSP.)will do the job with no problem but for the ultimate range These Hornady rounds are amazing https://www.budsgunshop.com/catalog/product_info.php/cPath/656_2081_10000571/products_id/52502/Hornady%2044%20Magnum%20LeverEvolution%20225%20Grain%20Flex%20Tip%20Expandin/