Yes, you can, but the products go through Shopify on the way. Shuttle doesn't send products straight from one Etsy shop to another. Instead, you bring the products into Shopify from your first Etsy shop, move them to your second shop in Shuttle, and then transfer them to Etsy.
Both Etsy shops need to be connected to Shuttle before you start.
Why do products need to be moved to the second Etsy shop?
A Shopify product can be linked to only one Etsy shop at a time. So when you transfer products from your first Etsy shop to Shopify, they stay linked to that shop.
While your second shop is active, Shuttle hides those products on the Shopify → Etsy tab and leaves them out of transfers to that shop. Some transfers also show the warning The product is assigned to a different Etsy shop.
Moving the products to your second Etsy shop before you transfer them fixes both.
Transfer products from one Etsy shop to another through Shopify
With your first Etsy shop active, transfer the products to Shopify.
Go to Settings > Account > Connected Shops and click Activate next to your second Etsy shop. Shuttle reloads with that shop active.
Go to Products, open the Shopify → Etsy tab and turn on All Etsy shops. Products linked to your first shop now show the label Linked to followed by that shop's name.
Move the products to your second shop:
For one product, click Move to Etsy shop on its row.
For several products, select them and click Move to Etsy shop… in the bar that appears.
For every product of your first shop, or every product in a Shopify collection, click Move products between shops….
Under Move to, choose your second shop. Click the move button, check the summary, then click Confirm move.
Transfer the products to Etsy. Because your second shop is active, they go there. If you ticked Add to queue in the move window, they are already in your queue.
What changes when you move products to another Etsy shop?
When you move products to your second Etsy shop:
The listings in your first Etsy shop stay as they are. If you no longer want to sell them there, deactivate them in Etsy.
Shuttle stops linking the Shopify product to the listing in your first shop, so that listing is no longer synced with it.
Reviews stay with the products.