measuring carry-over effects in mixed models

Hello All,

I'm analyzing the data from my longitudinal study whose design can be
depicted as (view the following in plain text):

O1  X1  O2  X2  O3  X3  O4
O1      O2      O3      O4

where Xs denote subtitled videos given to the treatment group and Os
denote measurement occasions.

My current model is:  lmer(y ~ time*group + [covariates] + (1 | student))

However, I'm also interested in measuring the "carry-over effects" of
watching subtitled videos at each occasion to the subsequent
occasions.

For instance, I want to know how much watching the subtitled video at
the first occasion (O1) impacts the treated students' performance at
later occasions (O2 and O3) etc.

I wonder if any changes to my model can enable me to measure these
carry-over effects or if any other R package may provide such
functionality?

Many thanks,
Simon