How to convert expression with Subscript to string

how to convert a expression containing 2D format into corresponding string that retains the format programmatically? For example, how to convert

{a^b + 1, 1.23*10^2, 2 Subscript[a, b]}
(* Please Press Ctrl+Shift+N to convert it to standard form *)

to

{"\!\(\*SuperscriptBox[\(a\), \(b\)]\)+1", "1.23\[Times]\!\(\*SuperscriptBox[\(10\), \(2\
\)]\)", "2\!\(\*SubscriptBox[\(a\), \(b\)]\)"}

The easiest way is to prevent evaluation of the expressions what can be done with Unevaluated and HoldAll. First, define the function

toString = Function[expr, ToString[Unevaluated@expr, StandardForm], HoldAll];

Now you can simply apply this function to an expression:

You can Map it over the list for obtaining separate string for every expression in the list:

Or you can make this function Listable and it will thread over the lists automatically:

toString = Function[expr, ToString[Unevaluated@expr, StandardForm], {HoldAll, Listable}];

Obtaining the box form from FullForm[ToBoxes["t1"]] (that's t subscript 1) - the box form can be used in a function like so:-

make[x_, n_] := 
 ToExpression[
  StringJoin["\"\\!\\(\\*SubscriptBox[\\(", ToString[x], "\\), \\(", 
   ToString[n], "\\)]\\)\""]]

make[t, 1]

make[t, 1] == "t1" (* again, t subscript 1 *)

True

To convert a subscripted variable another function can be used:-

f[x_] := Module[{a, b},
  a = x[[1]];
  b = x[[2]];
  make[a, b]]

f[t1]

"t1"

To convert an expression such as the following more manipulations will be needed.

expr = s + Subscript[t, 1] + u (* Hold can be used to preserve the order *)

s + u + t1

The problem is a matter of manipulating the output from this ...

ToBoxes[expr]

RowBox[{"s", "+", "u", "+", SubscriptBox["t", "1"]}]

... to the output here:

ToBoxes["s+u+t1"] (* expr with t subscript 1 pasted into quotes*)

(* "\"s+u+\\!\\(\\*SubscriptBox[\\(t\\), \\(1\\)]\\)\"" *)

For this example the manipulation can be done like so:

z = ToBoxes[expr];

ToExpression[
 StringJoin["\"",
  First[z] /. SubscriptBox[a_, b_] :>
    StringJoin["\\!\\(\\*SubscriptBox[\\(", a, "\\), \\(", b, "\\)]\\)"],
  "\""]]

"s+u+t1"

The output here includes t subscript 1.