Witold, for categorical data WLSMV would be an option. Previous research

suggests that WLSMV commonly performs better than ML with fewer than five response categories:

Rhemtulla, M., Brosseau-Liard, P. & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods in non-ideal conditions. Psychological Methods, 17, 354-373.

There is in article in the journal Structural Equation Modeling in which measurement invariance was tested using MLR and WLSMV:

Sass, D.A., Schmitt, T.A., & Marsh, H.W. (2014) Evaluating Model Fit With Ordered Categorical Data Within a Measurement Invariance Framework: A Comparison of Estimators. Structural Equation Modeling, 21 (2), 167-180. DOI: 10.1080/10705511.2014.882658

Kind regards,

Karin

Witold, for categorical data WLSMV would be an option. Previous research

suggests that WLSMV commonly performs better than ML with fewer than five response categories:

Rhemtulla, M., Brosseau-Liard, P. & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods in non-ideal conditions. Psychological Methods, 17, 354-373.

There is in article in the journal Structural Equation Modeling in which measurement invariance was tested using MLR and WLSMV:

Sass, D.A., Schmitt, T.A., & Marsh, H.W. (2014) Evaluating Model Fit With Ordered Categorical Data Within a Measurement Invariance Framework: A Comparison of Estimators. Structural Equation Modeling, 21 (2), 167-180. DOI: 10.1080/10705511.2014.882658

Kind regards,

Karin

Since your measurement model was chosen using WLSMV, measurement invariance should be tested using the same estimation method. I can't find a reason why not. On the contrary, if another method (ML/MLR) is used instead, the fit indices, e.g. for for configural invariance, probably won't be within acceptable limits.