Forcing class imbalance to mirror the target data
Disclaimer: I am assuming that by "source data" you mean the data you are using for training and by "target data" you mean the real world data the model will aim to classify. 

SMOTE Is usefull when your data is highly imbalance i.e. 1% A/ 99% B or something around this proportions. In your case I would expect the model to work just fine when classifying a different distribution of data as long as you have enough training examples in each class. If this approach doesn't work you can use cost sensitive learning to fit the imbalance but I would consider this a secondary path