Disclaimer: I am asking on behalf of my friend, so I can not give many specific information. Still, I hope the information provided will be enough to give advice.
Let's say that a person got a position as a PhD candidate in a ok lab in Europe a bit less than a year ago. After a few months, the person realized that the current PhD project is not a good match for her (language barriers, communication problems, different work approach and pace from majority of the lab...).
After considering the situation, the person decided to apply for a few a different PhD projects in North and South America where the topics are a better fit, and where it is less likely to have language problems (the person found some open applications and researched them on her own time, while still working normally for her current position).
While finishing writing the applications and cover letters, a dilemma emerged about at which point should the person mention (if at all) the current involvement in a position as a PhD candidate? Fully aware that lying is not an option, the basic dilemma is weather to mention it in the cover letter or the first interview (if it comes to that). (The CV format required for most applications is such that the current PhD position is not readily apparent).
Basically, the questions would be:
whether to mention the current position as a PhD candidate in the cover letter / application, or at some later point in the process?
when mentioning the current position as a PhD candidate, how much detail about the current position (and reasons for looking for a new one in order to leave the current one) is the right amount of detail?