The pair completed their moves on Monday afternoon.
It will be a second loan spell with AGF for the 21-year-old Grabara after he made 16 appearances and kept six clean sheets at the club during the 2018/19 season, reports the Liverpool Echo.
The talented young shot stopper signed a new long-term contract with Liverpool upon his return from Denmark and spent the whole of last season on-loan at Huddersfield Town - impressing for the Championship club and making 28 starts as they kept their place in the highly competitive division.
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