SQL Server - Copying a key from one table to another
For permanent reused code like this, you really should be explicitly defining your temporary table definitions.  If you are looking for an easy way to do that, please see below.  I'll also include information on your actual question.

Easy way to generate table definition:


locate the object in object explorer 
right click on it and select "script --> create table --> to SSMS window"


This should generate a new SSMS window with the table you selected scripted there.  Depending on your options, you will have indexes as well at the bottom.  

To make it a temporary table, just change the name of the table.  

Remove IDENTITY

Locate the identity column and remove the identity definition more than likely "IDENTITY(1,1)".

Example:

CREATE TABLE #INS
(
MyIdentityID INT NOT NULL PRIMARY KEY
, MyValue VARCHAR(100) NOT NULL
)


Please note, this is a simple and straightforward method that directly answers your question.  Any use of temporary tables in triggers makes me suspicious and I would like to know the full business reason behind it; it's possible that a better solution exists.