H4 holder is not authorized to work.
H4 can be converted to L1, provided the beneficiary has worked for that employer in any of its foreign branch for continuous 1 year within the last 3 years of entering the US. If your wilfe employment history this condition, she could move to L1.
Also to qualify, the named employee must
Generally have been working for a qualifying organization abroad for one continuous year within the three years immediately preceding his or her admission to the United States