Not sure what problem you are having but a grip that fits the 4056TSW will also fit the 4013TSW & Shorty 40, & vise-a-versa.
I have all three models also.
All I can suggest is that sometimes new grips are extremely tight to get on the first time & require some cussing to help them along.
Again, all three use the same grips & magazines.
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Waiting for the break of day
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