GLMER: Figuring out for which group a predictor is significant - is this correct?

I have a dataset containing the results of a categorization test, where two groups of participants (all native speakers of French learning English) choose one out of two categories after listening to a given English vowel. The variables included in the dataset are:

id - subject's id.

Group - two different learner groups (A and B).

stim -the English vowels that are given as stimuli.

vowel - Vowel category of the stimulus: whether it is a front vowel (e.g. the one in the word "bed") or back vowel ( e.g. the one in the word "cut")

RESP - How the participant categorized the vowel using their native language inventory. The options are either /a/ or /e/

I used a generalized linear mixed effect model to investigate whether there is an interaction between vowel and Group regarding the choice of RESP. The model with the optimal fixed- and random-effects structure looks a follows:

glmer1<-glmer(as.factor(RESP) ~ Group*vowel + (1|id), data=data, family="binomial")

Now I am trying to find out for which of the both groups the vowel was a significant predictor for RESP.

However I am uncertain if my approach is correct and would like some feedback.

I have divided the dataset into two subsets (one for each group) Then I have created two glmers with RESP as the dependent variable and vowel as the predictor, each using one of the subsets as data.

The Anova() output for both models A.glmer and B.glmer shows that vowel is a significant predictor for RESP (p<0,05) ,which would mean vowel is a singnificant IV for both groups A and B.

Could this be correct?

groupA= subset(data, Group== "A")
groupB= subset(data, Group== "B")

A.glmer<-glmer(as.factor(RESP) ~ vowel + (1|id), data=groupA, family="binomial")

Anova(A.glmer, type="III")

Analysis of Deviance Table (Type III Wald chisquare tests)

Response: as.factor(RESP)
Chisq Df Pr(>Chisq)
(Intercept) 10.574 1 0.001147 **
vowel 24.614 1 7.003e-07 ***
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Analysis of Deviance Table (Type III Wald chisquare tests)

B.glmer<-glmer(as.factor(RESP) ~ vowel + (1|id), data=groupB, family="binomial")


Response: as.factor(RESP)
Chisq Df Pr(>Chisq)
(Intercept) 6.6026 1 0.01018 *
vowel 18.1209 1 2.073e-05 ***
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1