Here's a three-sentence answer:
The narrator of the epic poem Beowulf is Christian, but Beowulf sure isn't. If Beowulf goes anywhere when he dies, it's into the immortal realm of legends and heroes. The Germanic people that Beowulf represents didn't have a Christian afterlife; they saw as immortality as something secured by being so great (incl. killing humans better than anyone else) in this world that people would continue to talk about them even after they're long dead.
If that's not enough, here's some more:
Beowulf's a character out of the pagan Germanic past that was carried over to England when the Angles, Saxons, and Jutes (among other, smaller groups) swept into the island from mainland Europe to fill the power vacuum left by the retreating Romans. That pagan past didn't disappear when Christianity spread across England.
In the epic poem "Beowulf" Grendel is the creature. Grendel has killed and maimed men.
"but the murderous man-bane"
In the biblical text Heaven would not be open to the creature but to Beowulf. Grendel, Beowulf’s adversary was believed to have come from Middle Earth (hell), his defeat of her would have meant that he had done God's work. There is mention of the Lord's will being on the side of the men and Beowulf.
Another element that address Beowulf’s afterlife are the elements of the Christian philosophy at the time of the poem. It was as follows; man only survives as it is God's will, man that does God's will is to be enshrined in the Heaven's, and all earthly gifts flow from God. Beowulf met those obligations when he conquered the hellish beast.