Step 1. Open template file: pdf/invoice.addresses-tab.tpl

Step 2. Remove shop address and change width for both delivery and invoice address to 50%

<table id="addresses-tab" cellspacing="0" cellpadding="0">
 <tr>
    <td width="50%">
       {if $delivery_address}<span class="bold">{l s='Delivery Address' pdf='true'}</span><br/><br/>
         {$delivery_address}
       {/if}
    </td>
    <td width="50%"><span class="bold">{l s='Billing Address' pdf='true'}</span><br/><br/>
       {$invoice_address}
    </td>
 </tr>
 </table>

Step 3. Save template file to your themes folder eg. themes/<your theme>/pdf/invoice.addresses-tab.tpl

Here is a screenshot what the invoice header looks like after the shop address is removed.