Do I keep pre-installed games when transferring from one 3DS to another?

According to Nintendo's own FAQ (Click General Information -> What Is Transferred During the System Transfer Process?), you will keep your game on the target system, and be able to redownload it from the eShop, see the two excerpts from the answer:

What Is Transferred During the System Transfer Process?
Applies To: Transfer From Nintendo 3DS
Answer:
For the most part, information on the target system (system being transferred to) will be overwritten by the information on the source system (system being transferred from). See below for specific details, or click here for more information:
- All content downloaded via the eShop on both systems (DSiWare, Ambassador games and status, 3DS Downloadable software, etc) will be combined together onto the target system.
- After the transfer is complete, titles will be available to re-download from the Nintendo eShop on the target system.
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- Pre-installed games [...] are treated as a standard Nintendo eShop game license.
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