|You'll have to adjust this formula to fit your exact layout, but the concept works.|
Since we don't know anything about the layout of your sheets, or where on Sheet 1 you wanted to enter 63, I wrote a formula that actually looks at Sheet2!B1 for the value and populates Sheet2 Column A with the data from Sheet1.
For testing purposes, it also assumes that your Client Numbers reside in Sheet1!A1:D1. Again, adjust as required.
Enter this formula in Sheet2!A1 and drag it down as far as you need it:
How it works:
MATCH(Sheet2!$B$1, Sheet1!$A$1:$D$1, 0)
This will look for the value in Sheet2!B1 within the range Sheet1!$A$1:$D$1.
It will return the relative location of that value. For example, if the value is found in column 2 of that range, it will return 2. Note that I don't mean Column B, I mean column 2 of the lookup_array.
MATCH(Sheet2!$B$1, Sheet1!$A$1:$D$1, 0) - 1
This will reduce the value returned by the MATCH function by 1.
ROW()-1 will return the Row number of the cell that the formula resides in, minus 1.
For example, if =ROW()-1 is in Row 1, it will return 0. As you drag the formula down the column, it will increment and always return a value that is 1 less than the Row it resides in.
Now, the OFFSET function requires a starting location (reference) and a rows and cols argument. It will return the value from the cell that is offset from the starting location by that many rows and columns.
So, by starting in A1 and using ROWS()-1 as the rows argument and the MATCH(...)-1 as the cols argument we get the values from the matching column.