Will change in standard deviation impact covariance?

If we increase the degree of standard deviation of one variable, does it affect covariance of two variables? Example, two variables are there, A & B, the covariance of A & B is 100, and the degree of standard deviation of A is 12, let say, if the degree of standard deviation of A is increased from 12 to 18, is there any changes in covariance of A & B? If I ask question in another way, then, if slope of A & B is 1, and degree of standard deviation of A is 12, what is new slope of A & B if degree of standard deviation of A increases from 12 to 18?

You're making a transformation on $$A$$ and get another RV $$X=f(A)$$. This can be simple scaling or any other operation. The covariance between the newly transformed variable $$X$$ and $$B$$ will in general change, i.e. in general, we have$$\operatorname{cov}(A,B)\neq \operatorname{cov}(X,B)$$
A simple example would be scaling, $$X=2A$$:$$\operatorname{cov}(X,B)=\operatorname{cov}(2A,B)=2\operatorname{cov}(A,B)\neq \operatorname{cov}(A,B)$$ in general.