the engines will swap as the mounting points are the same.
1.5 Hp will make no difference.
Naturally the control cables & wires will need to be modified cause the plugs are differeint,
The major concern will be the alternator,
If both mowers have manual blade engagement all is fine, If the Craftsman is electric & the Husqvarna is manual all is fine.
However if the Husky has an electric blade clutch & the craftsman is manual then the Brigs engine will need an alternator upgrade or you will need a battery charger to recharge the battery between mows cause the alternator will not be able to keep up.