I have two sets of observations for performing Bayesian inference. Since the algorithm takes some time to deal with all the observations together, I was wondering if is there a way to use the posterior from the first analysis as prior for the second (some of the parameters’ distribution are not very simpled-shaped).

From the theoretical point of view there is no problem: the posterior is equal to the prior multiplied by the likelihood function, and the latter is usually the product of a distribution evaluated at all data points. So if you split the data into two parts and use the first posterior as a prior for the second data set, this is equivalent to use all the data at once.

In UQLab you define a parametric prior, and you usually obtain the posterior as sample sets. So you would need to use the inference module of UQLab to fit the best distribution to your first posterior data.