Knowledge of fiber parameters is paramount for efficient fiber optic communication. We investigate the suitability of a recently proposed Koopman operator-based parameter estimation method for partial differential equations for the identification of single-span fiber links of various lengths in simulations. The Koopman-based identification method does not require spatial derivatives, which makes it especially suitable for the estimation of fiber parameters. The method also does not require specific training signals or devices. It can estimate the parameters using transmitted and received signals from an operational link. We identify the dispersion length as a critical parameter for the accuracy of the method and show that it can jointly identify the fiber parameters at optimal transmit powers for four different fiber types, with the worst relative error below 20% in identifying the Kerr parameter. The loss and dispersion coefficients are identified more accurately in all the scenarios considered with relative errors below 5%. We also compare the algorithm against other fiber parameter estimation techniques, such as conserved quantity identification and direct identification (based on discretization of the spatiotemporal domain). We finally demonstrate that the algorithm detects changes in the fiber parameters more accurately than the parameters themselves, which can be exploited for link monitoring.