Can we construct exact analog signal at receiver as same as the source from the sampled signal?
In theory: No we can not. For a signal to be sampled accurately it needs to be band limited. In order to be band limited it needs to be infinite in time and that doesn't exist.
In practice: sure we can. For any given level of accuracy, signal spectrum and bandwidth of interest it's pretty straight forward to find sampling parameters (rate, bit depth) that will do.
This boils down to your definition of "exact".