Hello Marine,
As Profit center is always derived either from cost center or from material or from account assignments, it is not recommended to manually input profit center at the time of GR.
If any manual assignment required for GR there are two ways of achieving :
1 - enter proper account assignment in PO itself
2- BTE (1120 will be appropriate) or substitution or Enhancement Spots can be used by the help of abaper to capture manual profit center mentioned in GR.
Thanks,
ram