`Get` files depending on the string input [duplicate]

Question

Let's suppose I have a code like this:

ClearAll["Global`*"]
a = 2;
b = 3;
Sab=*lots of calculations on a and b*
Save["S" <> ToString[a] <> "" <> ToString[b] <> ".m",{Sab}]

This codes construct the set Sab for a=2 and b=3 and saves a file called "S23.m". Now... I have another code like this:

ClearAll["Global`*"]
a = 2;
b = 3;
Sab=*lots of calculations on a and b*
* . . . Lots of calculations on Sab . . . *
* . . . Some results . . . *

I would like to use Get in the second code to use the sets Sab that were previously calculated, so I wouldn't need to calculate them again, but these files depend on the inputs a and b. I tried, for example,

<< "S" <> ToString[a] <> "" <> ToString[a] <> "half.m"

but it doesn't work. How can I do it?