You can do that on server side :
RegisterStartupScript("MyScript", "<script language=javascript>document.getElementById('" + txtBox.ClientID + "').value = document.getElementById('divvalue').innerHTML;</script>");
I think that the mistake you have made is to put your script before the textbo.
When page load , javascript try to execute the code by do not know yet the textbox control and the div.
To be sure that a javascript is executed when all your page is loaded (or DOM built) add defer="defer" on javascript tag
<script language=javascript defer=defer>
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