Let us assume that I have applied for a post doc position in place X on a project Y in collaboration with university Z, and they asked for a personal statement.
A week later, another post doc position appeared in place Z on the same project Y and in collaboration with university X.
Since I am very interested in the project, I'd like to maximize my opportunity to obtain the position on the project and I'd like to apply to this second position as well.
Do you think I should say this to the prof. related to my first application (since it might be that they are in contact and exchanging information)?
And a second question regards the personal statement: in the second post-doc position, they ask o a letter of motivation. How bad is if I just copy and paste the previous letter (just changing the properly the name of the institution inside)? I mean, I wrote the letter for the same project, my motivation are there, but I was wondered that they might exchange information and this might look bad.
Since these are my first post-doc application I don't really know how they used to manage these things..