Can I transfer shortened links from one service to another?

Short links are a technology in which the original long link is assigned its short counterpart within the namespace available on a particular domain (surl.li. bit.ly). In other words, you ask a specialized service to add your long link to their database and create a short analog for it. This way, when a user clicks on the short link, the shortener's servers will redirect you to the original link.
Let's imagine that you have shortened 100 short links on the surl.li shortener through your personal account. But for some reason, you want to switch to the surl.lu shortener. At the same time, all your 100 short links have long been posted on websites, social networks, sent out in messengers, and you cannot replace them. So can you change the shortener while leaving all the links unchanged?
In most cases, except for one, this is not possible. If your shortlinks are served on the surl.li domain, all request processing logic remains with this shortener.
So you can create 100 new links on a new shortener and it will contain a new domain and you will need to replace all previously hosted links with new short links.
Can there be an exception? Yes!
If the shortlink service supports the use of custom domains, i.e. registered domains “for you”, you can indeed change the shortener even without changing the already placed shortlinks. To do this, several conditions must be met:

You must have a registered domain name in your control. it can be either a domain registered with the shortener or a domain with a third-party registrar;
The old and new shorteners must support the function of creating short links on the custom domain;
The method of managing the custom domain on the old and new service must be the same

In this case, you can easily transfer the domain itself to the service and continue working with all your links. To do this, simply request the data from your current shortener or upload a csv file with your links. This is especially useful when it comes to thousands and hundreds of thousands of links.
By the way, this kind of transfer is a great opportunity to clean up your database from temporary and outdated links. After all, when you shorten within 1 domain, the space and variability are also limited to 1 domain only