I am not aware of any standard report, but I am not much familiar with both, serial numbers and handling units.
SER06 has the link between HU and serial numbers.
The serial number itself is in the object list of the HU, this object list ist table OBJK.
So you need to find your serial number in OBJK, then you take the content from field OBKNR and search in table SER06 to get the Handling unit for the object list.