Sophia here from Shopify. Welcome to the Shopify Community!
Oberlo doesn't sync AliExpress shipping methods to Shopify. Instead, it's recommended that you set up your own shipping rates. There are a couple of strategies to consider, one being charging a flat rate for shipping, and the other being factoring your shipping costs into product prices and offering free shipping.
Full details can be found here: Set up your Shopify shipping settings. Please let me know if you have any questions about what's covered in that document.
thank you very much for your answer.
So is there any other Dropshipping app (even if paid) that allows this functionality of reproducing the shipping data from the supplier directly to my customer?
I'm not familiar with any dropshipping apps that pull shipping rates from the suppliers into your Shopify shipping settings. I took a look at a couple of the other popular options—Modalyst and Spocket—but their recommendations are similar to Oberlo's in that they advise setting up your own rates. Modalyst's help documents mention that they offer a feature allowing you to automatically add shipping costs to your product price.
If you're looking at single suppliers, that's a bit different. For example, print on demand apps like Printful produce and ship the product for you. Therefore, they have their own shipping rates and can send them to Shopify using carrier calculated shipping and an app like Advanced Shipping Rules. It gets complicated with dropshipping apps because they would be pulling rates from potentially hundreds or thousands of different suppliers whose country of origin and shipping carriers vary.
Offering flat rates or free shipping simplifies things for you as well as for your customers. You can either price your products strategically to ensure you're covered for the range of shipping costs that your suppliers charge, or set flat rates that cover that range. Customers typically appreciate knowing ahead of time what they'll pay for shipping, so you could see a higher conversion of sales if you're clearly communicating to customers that shipping is free or if you have flat rates listed so they know what they'll pay based on their order before they get to the checkout.