Hello,
I realise this topic is likely old enough for you to have dropped the repair or found another solution.
You'll find plenty of useful information on the STK8050 HERE including internal schematic but it looks as if you found that and were puzzled because it did not match your module. (Beware: Chinese copy may have used a Sziklai pair in which case your 2SA1303 will not fit... I don't know never tried repairing these fake modules...)
Output transistor Emitters lead to pin 3 through low value resistors (if they exist on your Chinese copy of STK, this is not original component you have) collectors (bulky metal squares) lead to pins 1 and 5 that leaves you with the bases going to 11 and 21, make sure the next transistors down the line are not dead too...
If you want a neater / more reliable repair I still have several of my copies of this component (page 7 of above link).
I realise this topic is likely old enough for you to have dropped the repair or found another solution.
You'll find plenty of useful information on the STK8050 HERE including internal schematic but it looks as if you found that and were puzzled because it did not match your module. (Beware: Chinese copy may have used a Sziklai pair in which case your 2SA1303 will not fit... I don't know never tried repairing these fake modules...)
Output transistor Emitters lead to pin 3 through low value resistors (if they exist on your Chinese copy of STK, this is not original component you have) collectors (bulky metal squares) lead to pins 1 and 5 that leaves you with the bases going to 11 and 21, make sure the next transistors down the line are not dead too...
If you want a neater / more reliable repair I still have several of my copies of this component (page 7 of above link).