You cannot realize material to material transfer if the base unit of measures differ from each other - according to my best knowledge.
(stockkeeping unit = base unit)
You can use MB1A + 201 to eliminate the stock of one of yours material, and via MB1A + 202 you can set the stock level of the other material. The result is the same.
As you said, Material 1 is measured with KG and Material 2 is measured with ST. But let me know these two units of measure are base unit of measure or order unit. Please confirm the above.
If both materails unit of measure (i.e. you mentioned UoM) is base unit of measure means. You can do the material to material stock transfer, once after you maintain the conversion factor of unit of measure in the material master. (i.e. Goto Additional Data in the Material master through change materail master MM02. And give the conversion between these two UoM's and then try for the M to M transfer through T.Code: MB1A, with Mvt.type. 309.
Suggestion: But, I don't think it is possible (i.e. M to M transfer with each different UoM). However you just try for the above process and will make you understand.
Hope this will clarify you,
Reward, if it helps,