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Is there an expression for the blanks in the following situation?

You have a friend who isn't from where you're from and speaks in an accent different from yours. At first you feel strange with it, but as you talk with him for months you get adapted. One day you happen to say something in his accent (or use an expression he often uses), and then say,

"Oh, your accent ____ me."

or

"Come on, since you always say, your words ____ me."

In my mother tongue, both blanks are filled by a word corresponding to "transferred to", but I'm assuming it would be awkward because it's a direct translation. I'd like to know if there's a verb or a phrase that fits the situation.

Thank you.

Try: "Your accent rubbed off on me."

rub off on (someone)

To have one's characteristics, mannerisms, or behavior be adopted by someone with whom one has spent a lot of time. Peter's been very unruly lately. I think that new kid is rubbing off on him. It seems like your boss's greed is rubbing off on you—is money all you care about now?

https://idioms.thefreedictionary.com/rub+off+on

This doesn't fit as well in the second sentence because, as the definition I quoted says, we tend to use this expression to talk about mannerisms, or behavior. Words wouldn't really rub off on someone. But a way of speaking can rub off on someone.

I'm not sure how well it fits your sentences, since it's more technical than you probably want, but in psychology this is called mirroring. The linked wikipedia article describes it:

Mirroring is the behaviour in which one person subconsciously imitates
the gesture, speech pattern, or attitude of another.

In communication, the behavior you're describing would be called convergence. The key action would involve converging in speech pattern or (more generally) accommodating another's speech pattern.

The concept is a large part of Communication Accommodation Theory, developed in the early 1970s by Howard Giles. It's a framework that predicts factors for people making their speech more similar to a conversational partner (convergence) as well as more different from that partner (divergence). This 2007 entry for CAT in Explaining Communication: Contemporary Theories and Exemplars provides an overview of the theory as a whole.

Within this theory, convergence is a subconscious strategy of adapting to the speech patterns of one's interlocutor. That can be motivated by several factors, including a desire to gain acceptance with the people we're talking to. In contrast, divergence can be a way of maintaining one's ties to a prior identity, like a politician maintaining or even exaggerating the speech patterns of the region they represent when they speak to colleagues with other accents and patterns.

Within this research, converge and accommodate are used as verbs to describe this behavior. For example:

Bourhis, Roth, and MacQueen (1988) found that physicians , nurses,as well as hospital patients considered it more appropriate for health professionals to converge to the patients’ everyday language than to maintain their medical jargon.

...

This has been observed in a number of settings also where, for example, a travel agent accommodated her pronunciation to the different socioeconomically based language styles of her Welsh clientele (N. Coupland, 1984) and, in Taiwan, where salespersons converged more to customers than vice versa (van den Berg, 1986).

So to take your example sentences, you could say:

Oh, your accent converged with mine.

Come on, your words accommodate mine.