That's a nasty conundrum. It's pretty grim when a client has misplaced, deleted or otherwise lost a key identity asset.
There is a way to recover in Photoshop, since you say that the logo is a solid. You already know the PMS color, so the procedure is to isolate the bevel and drop shadow effects and make them a Black spot color, then create a spot channel for the PMS color that is 100% where the color is solid and gradiently fades where the "highlight" would be in the bevel. It's not a straightforward process, in fact it's a tedious workaround, but if you're truly stuck this is a way to do it.
I've taken an old NASA logo that I've rasterized and added effects to, to demonstrate the procedure:
Here's our starting point, a solid color logo with effects applied, with no background. (Note: The drop shadow is best applied newly in Illustrator, so I'm ignoring it here.)
In the Layers Panel flyout menu, choose
Create Layers. This will give you two Bevel layers clipped to the logo and a drop shadow below. You can delete the drop shadow layer.
Target the logo layer and set the Fill to 0, so that only the effects are visible. Select All (
Ctl/Cmd-A) and Copy Merged (
Ctl/Cmd-Shift-C) then deselect. (You MUST deselect!)
Open the Channels panel, and from the flyout menu choose
New Spot Channel
Set the Color to Pantone Black 6 C from the Pantone Solid Coated book, and the Solidity to 100%.
Make sure the new channel is targeted, then Paste and Deselect. You may have to nudge the new channel to get an exact registration.
In the Layers Panel, set the Fill of your logo layer to 100% and turn off the Drop Shadow layer (you don't want that to affect the next step).
In the Channels Panel, turn off the Spot Channel.
At this point you should see only the flat logo with the Bevel/Emboss.
- In the Channels Panel, find a CMY channel that has good contrast, with a solid black where the color should be.
Ctl/Cmd-Click that channel to load its opacity as a selection, then invert the selection.
From the flyout menu, again choose New Spot Channel, and make it the PMS color of your logo. I used something completely different, to make the effect obvious.
In the Layers Panel, turn off the logo layer.
You now have a logo and effects in two spot colors, one of which is really just process black.
At this point set the fill of the logo layer back to zero.
Save As file type DCS 2.0 (a form of EPS).
When you place this in Illustrator, the spot colors will come along for the ride if not there already. Your print provider's prepress folks can map the PMS Black to process black, or you can export to PDF and do it in Acrobat.