${\rm Fun}^R(C_1^\text{op},C_2)$ is a presentable category

${\rm Fun}^R(C_1^\text{op},C_2)$ is a presentable category

I am stuck in proving Lemma 5.25 in Moritz Groth's notes: I am asked to
prove that for any two presentable categories $C_1,C_2$ the category of
limit preserving functors ${\rm Fun}^R(C_1^\text{op},C_2)$ is again
presentable.
Groth solves the particular case $C_1=[E_1^{op},{\bf Sets}]$, appealing
thm 2.39 in Adamek-Rosicky's book; then he says "With some more effort the
general case can also be established./p pThe proof given by Groth in that
particular case seems to rely on the equivalence
$Adj(\widehat{E_1},C_2^{op})\cong Fun(E_1,C_2^{op})$ established via
nerve-realization, so I'm not able to generalize it./p pWhat is the idea
behind the general case?/p