There is research on the links between downward social mobility and happiness, however:
These empirical studies show little consensus when it comes to the consequences of intergenerational social mobility for SWB: while some authors suggest that upward mobility is beneficial for SWB (e.g. Nikolaev and Burns, 2014), others find no such relationship (e.g. Zang and de Graaf, 2016; Zhao et al., 2017). In a similar vein, some researchers suggest that downward mobility is negatively associated with SWB (e.g. Nikolaev and Burns, 2014), while others do not (e.g. Zang and de Graaf, 2016; Zhao et al., 2017)
This paper suggests that differences in culture may influence the connection between downward social mobility and happiness:
the United States is an archetypical example of a success-oriented society in which great emphasis is placed on individual accomplishments and achievement (Spence, 1985). The Scandinavian countries are characterized by more egalitarian values (Schwartz, 2006; Triandis, 1996, Triandis and Gelfand, 1998; see also Nelson and Shavitt, 1992)...A great cultural salience of success and achievement may make occupational success or failure more important markers for people’s SWB.
And they claim to find this:
In line with a previous study from Nikolaev and Burns (2014) we found that downward social mobility is indeed associated with lower SWB in the United States. This finding provides evidence for the “falling from grace hypothesis” which predicts that downward social mobility is harmful for people’s well-being. However, in Scandinavian Europe, no association between downward social mobility and SWB was found. This confirms our macro-level contextual hypothesis for downward social mobility: downward social mobility has greater consequences in the United States than in the Scandinavian countries.
This is, of course, just one study so not very conclusive.
Epistemic status: Uneducated guesses, however I'm more confident than usual for uneducated guesses that this points at a real effect, much less confident about effect sizes.
Great question! I don't know the literature enough to provide a useful answer. However I think your friend may be framing this question incorrectly.
To the extent that we observe a correlation between income and happiness, and correspondingly decreased happiness from downwards social mobility, I think it is too hasty to jump to the conclusion that this is entirely or even primarily due to habituation to a wealthier lifestyle/material goods. Here are two other hypotheses:
1) seems clearly plausible to me. Income is pretty frequently used as a proxy for social status,* both in our intuitive understanding of the world and in formal literature (hence phrases like "socioeconomic status", "social mobility," etc). So I think it's plausible that a lot of the effects of observed income on happiness (and perceived dissatisfaction from downwards mobility) comes from a perceived gain(loss) of status, rather than from the gain(loss) of desired material goods or lifestyle.
1) will predict that people who willingly choose a lower-paying but equally (or more) socially desirable career than their parents will not be (much) less happy, and indeed may be happier. For example, people who willingly become academics, artists etc.
2) is less obvious, but also intuitively seems significantly more likely than not. For example, certain physical and mental disabilities (eg debilitating pain) likely reduces both your ability to earn significant income, and directly makes you less happy. Some environmental factors may do the same. More cheerily, traits that make people more well-liked may also makes people happier, even after you factor out the social aspects.
So you can think of social status both directly causal of happiness, but also having bidirectional effects with underlying environments/traits that are themselves causal of happiness.
To the extent that they're true, 1) and 2) may have implications for EA (not all of them positive). I can write out more speculations in a separate comment if people will find it helpful.