I know we can save phenotype, feature and expression data of a expression set separately in a text files. I want to know if it's possible to save the expression set into a folder and then open it later for other applications?

You could just save it as an RDS object. Here is an entirely reproducible example:

Download a GEO study

library(Biobase)
library(GEOquery)
gset <- getGEO("GSE89231", GSEMatrix =TRUE, getGPL=FALSE)
if (length(gset) > 1) idx <- grep("GPL570", attr(gset, "names")) else idx <- 1
gset <- gset[[idx]]

gset
ExpressionSet (storageMode: lockedEnvironment)
assayData: 54675 features, 49 samples 
  element names: exprs 
protocolData: none
phenoData
  sampleNames: GSM2361446 GSM2361447 ... GSM2361494 (49 total)
  varLabels: title geo_accession ... cell line:ch1 (35 total)
  varMetadata: labelDescription
featureData: none
experimentData: use 'experimentData(object)'
Annotation: GPL570

Save the ExpressionSet object to an RDS file and remove the object from the workspace

saveRDS(gset, 'MyExpressionSet.Rds')
rm(gset)
gset
Erro: objeto 'gset' não encontrado

Read it back in

gset <- readRDS('MyExpressionSet.Rds')
gset
ExpressionSet (storageMode: lockedEnvironment)
assayData: 54675 features, 49 samples 
  element names: exprs 
protocolData: none
phenoData
  sampleNames: GSM2361446 GSM2361447 ... GSM2361494 (49 total)
  varLabels: title geo_accession ... cell line:ch1 (35 total)
  varMetadata: labelDescription
featureData: none
experimentData: use 'experimentData(object)'
Annotation: GPL570