Hello
I can see two good ways of doing it (there are several possibilities):
1 - As the first reply, create a new program and transaction to build that same front-end as you see into Material Additional Data / Units of measure and then this front-end must call the BAPI_MATERIAL_SAVEDATA passing the values you want, If it's just an unit conversion you can pass by just the values below:
MARM-MATNR (Material number)
MARM-MEINH (Alternative unit of measure) - Bapi field ALT_UNIT
MARM-UMREZ (Numerator) - Bapi field NUMERATOR
MARM-UMREN (Denominator) - Bapi field DENOMINATR
2 - Use a tool like BRO (business rules organizer - www.hks-sa.com) where you can create a rule-based front-end and rule-based processing and releases to the user just the access to the activity "Add unit convertion factors".
Hope it helped.
Bruno